Integrate Refactor solver sources and dual MSVC CMake builds

.gitignore

@@ -27,3 +27,7 @@ phases/**/step*-output.json
 
 # local document backups and initialization state
 .dryforge/
+
+# direct MSVC and CMake local build state
+/.build/
+/msvc/Fesa.Local.props

CMakeLists.txt

@@ -1,13 +1,14 @@
 cmake_minimum_required(VERSION 3.25)
-
 project(FESA VERSION 0.1.0 LANGUAGES CXX)
-
 set(CMAKE_CXX_STANDARD 17)
 set(CMAKE_CXX_STANDARD_REQUIRED ON)
 set(CMAKE_CXX_EXTENSIONS OFF)
-
+set(CMAKE_MSVC_RUNTIME_LIBRARY "MultiThreaded$<$<CONFIG:Debug>:Debug>DLL")
+# Pin the original backend ABI/link/thread choices rather than package defaults.
+set(MKL_INTERFACE ilp64)
+set(MKL_LINK dynamic)
+set(MKL_THREADING intel_thread)
 include(cmake/FesaDependencies.cmake)
-
 find_package(Doxygen QUIET)
 if(Doxygen_FOUND)
   add_custom_target(fesa_docs
@@ -19,6 +20,5 @@ if(Doxygen_FOUND)
 endif()
 
 enable_testing()
-
 add_subdirectory(src/fesa)
 add_subdirectory(tests)

CMakePresets.json

@@ -3,11 +3,11 @@
   "configurePresets": [
     {
       "name": "windows-msvc-ninja-debug",
-      "displayName": "Windows MSVC x64 Debug (Ninja)",
       "generator": "Ninja",
-      "binaryDir": "${sourceDir}/build/windows-msvc-ninja-debug",
+      "binaryDir": "${sourceDir}/.build/cmake-debug",
       "cacheVariables": {
         "CMAKE_BUILD_TYPE": "Debug",
+        "CMAKE_EXPORT_COMPILE_COMMANDS": "ON",
         "FESA_GTEST_SOURCE_DIR": "$env{FESA_GTEST_SOURCE_DIR}",
         "MKL_DIR": "$env{MKL_DIR}",
         "TBB_DIR": "$env{TBB_DIR}",
@@ -16,11 +16,15 @@
     },
     {
       "name": "windows-msvc-ninja-release",
-      "displayName": "Windows MSVC x64 Release with symbols (Ninja)",
-      "inherits": "windows-msvc-ninja-debug",
-      "binaryDir": "${sourceDir}/build/windows-msvc-ninja-release",
+      "generator": "Ninja",
+      "binaryDir": "${sourceDir}/.build/cmake-release",
       "cacheVariables": {
-        "CMAKE_BUILD_TYPE": "Release"
+        "CMAKE_BUILD_TYPE": "Release",
+        "CMAKE_EXPORT_COMPILE_COMMANDS": "ON",
+        "FESA_GTEST_SOURCE_DIR": "$env{FESA_GTEST_SOURCE_DIR}",
+        "MKL_DIR": "$env{MKL_DIR}",
+        "TBB_DIR": "$env{TBB_DIR}",
+        "HDF5_DIR": "$env{HDF5_DIR}"
       }
     }
   ],
@@ -37,7 +41,17 @@
   "testPresets": [
     {
       "name": "windows-msvc-ninja-debug",
-      "configurePreset": "windows-msvc-ninja-debug"
+      "configurePreset": "windows-msvc-ninja-debug",
+      "output": {
+        "outputOnFailure": true
+      }
+    },
+    {
+      "name": "windows-msvc-ninja-release",
+      "configurePreset": "windows-msvc-ninja-release",
+      "output": {
+        "outputOnFailure": true
+      }
     }
   ]
 }

FESA.sln

@@ -0,0 +1,48 @@
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 18
+VisualStudioVersion = 18.0.0.0
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{BC8A1FFA-BEE3-4634-8014-F334798102B3}") = "fesa_solver", "msvc\fesa_solver.vcxproj", "{3AEC39D9-4641-5161-9107-265EB50CA882}"
+EndProject
+Project("{BC8A1FFA-BEE3-4634-8014-F334798102B3}") = "fesa_cli", "msvc\fesa_cli.vcxproj", "{6DE2CFFA-D9B3-5E14-BEBD-5DFAB2B5290B}"
+EndProject
+Project("{BC8A1FFA-BEE3-4634-8014-F334798102B3}") = "fesa_unit_tests", "msvc\fesa_unit_tests.vcxproj", "{42558F77-73F2-5CA7-8E3C-BB0E1646CD45}"
+EndProject
+Project("{BC8A1FFA-BEE3-4634-8014-F334798102B3}") = "fesa_integration_tests", "msvc\fesa_integration_tests.vcxproj", "{7770C26B-DBFE-505D-8788-8B7EFD9A5A70}"
+EndProject
+Project("{BC8A1FFA-BEE3-4634-8014-F334798102B3}") = "fesa_reference_tests", "msvc\fesa_reference_tests.vcxproj", "{330D2DFB-E57D-517D-A795-F1EA620B69F0}"
+EndProject
+Project("{BC8A1FFA-BEE3-4634-8014-F334798102B3}") = "gtest", "msvc\gtest.vcxproj", "{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|x64 = Debug|x64
+		Release|x64 = Release|x64
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{3AEC39D9-4641-5161-9107-265EB50CA882}.Debug|x64.ActiveCfg = Debug|x64
+		{3AEC39D9-4641-5161-9107-265EB50CA882}.Debug|x64.Build.0 = Debug|x64
+		{3AEC39D9-4641-5161-9107-265EB50CA882}.Release|x64.ActiveCfg = Release|x64
+		{3AEC39D9-4641-5161-9107-265EB50CA882}.Release|x64.Build.0 = Release|x64
+		{6DE2CFFA-D9B3-5E14-BEBD-5DFAB2B5290B}.Debug|x64.ActiveCfg = Debug|x64
+		{6DE2CFFA-D9B3-5E14-BEBD-5DFAB2B5290B}.Debug|x64.Build.0 = Debug|x64
+		{6DE2CFFA-D9B3-5E14-BEBD-5DFAB2B5290B}.Release|x64.ActiveCfg = Release|x64
+		{6DE2CFFA-D9B3-5E14-BEBD-5DFAB2B5290B}.Release|x64.Build.0 = Release|x64
+		{42558F77-73F2-5CA7-8E3C-BB0E1646CD45}.Debug|x64.ActiveCfg = Debug|x64
+		{42558F77-73F2-5CA7-8E3C-BB0E1646CD45}.Debug|x64.Build.0 = Debug|x64
+		{42558F77-73F2-5CA7-8E3C-BB0E1646CD45}.Release|x64.ActiveCfg = Release|x64
+		{42558F77-73F2-5CA7-8E3C-BB0E1646CD45}.Release|x64.Build.0 = Release|x64
+		{7770C26B-DBFE-505D-8788-8B7EFD9A5A70}.Debug|x64.ActiveCfg = Debug|x64
+		{7770C26B-DBFE-505D-8788-8B7EFD9A5A70}.Debug|x64.Build.0 = Debug|x64
+		{7770C26B-DBFE-505D-8788-8B7EFD9A5A70}.Release|x64.ActiveCfg = Release|x64
+		{7770C26B-DBFE-505D-8788-8B7EFD9A5A70}.Release|x64.Build.0 = Release|x64
+		{330D2DFB-E57D-517D-A795-F1EA620B69F0}.Debug|x64.ActiveCfg = Debug|x64
+		{330D2DFB-E57D-517D-A795-F1EA620B69F0}.Debug|x64.Build.0 = Debug|x64
+		{330D2DFB-E57D-517D-A795-F1EA620B69F0}.Release|x64.ActiveCfg = Release|x64
+		{330D2DFB-E57D-517D-A795-F1EA620B69F0}.Release|x64.Build.0 = Release|x64
+		{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}.Debug|x64.ActiveCfg = Debug|x64
+		{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}.Debug|x64.Build.0 = Debug|x64
+		{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}.Release|x64.ActiveCfg = Release|x64
+		{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}.Release|x64.Build.0 = Release|x64
+	EndGlobalSection
+EndGlobal

include/fesa/analysis/analysis_procedure.h

@@ -0,0 +1,23 @@
+#ifndef FESA_ANALYSIS_ANALYSIS_PROCEDURE_H_
+#define FESA_ANALYSIS_ANALYSIS_PROCEDURE_H_
+
+#include "fesa/analysis/prepared_analysis_outcome.h"
+#include "fesa/core/status.h"
+
+namespace fesa {
+
+class Domain;
+
+/// @brief Executes one prepared Domain without opening result files.
+/// @note The Domain and injected adapters outlive Execute. Accepted histories
+/// remain procedure-specific and are returned only after validation.
+class AnalysisProcedure {
+ public:
+  virtual ~AnalysisProcedure() = default;
+  /// @brief Returns the original typed completed payload or first failure.
+  virtual Result<PreparedAnalysisOutcome> Execute(const Domain& domain) = 0;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_ANALYSIS_PROCEDURE_H_

include/fesa/analysis/analysis_state.h

@@ -6,12 +6,13 @@
 #include <vector>
 
 #include "fesa/core/status.h"
-#include "fesa/fem/dof_manager.h"
 #include "fesa/math/vector.h"
 #include "fesa/results/result_records.h"
 
 namespace fesa {
 
+class DofManager;
+
 /// @brief Owns mutable quantities required by the V0 linear-static frame.
 class AnalysisState {
  public:

include/fesa/analysis/dynamic_execution_result.h

@@ -0,0 +1,19 @@
+#ifndef FESA_ANALYSIS_DYNAMIC_EXECUTION_RESULT_H_
+#define FESA_ANALYSIS_DYNAMIC_EXECUTION_RESULT_H_
+
+#include <vector>
+
+#include "fesa/analysis/dynamic_analysis_state.h"
+#include "fesa/core/diagnostic.h"
+
+namespace fesa {
+
+/// @brief Stores a complete HHT history before atomic result finalization.
+struct DynamicExecutionResult {
+  DynamicAnalysisState state;
+  std::vector<Diagnostic> diagnostics;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_DYNAMIC_EXECUTION_RESULT_H_

include/fesa/analysis/eigen_analysis_state.h

@@ -8,7 +8,7 @@
 #include <vector>
 
 #include "fesa/math/matrix.h"
-#include "fesa/solvers/eigen/mkl_feast_eigen_solver.h"
+#include "fesa/solvers/eigen/eigen_solver.h"
 
 namespace fesa {
 

include/fesa/analysis/hht_dynamic_procedure.h

@@ -1,10 +1,14 @@
 #ifndef FESA_ANALYSIS_HHT_DYNAMIC_PROCEDURE_H_
 #define FESA_ANALYSIS_HHT_DYNAMIC_PROCEDURE_H_
 
-#include "fesa/analysis/prepared_analysis.h"
+#include "fesa/analysis/dynamic_execution_result.h"
+#include "fesa/core/status.h"
 
 namespace fesa {
+
+class Domain;
 class LinearSolver;
+class NewtonIterationLogWriter;
 class ParallelFor;
 class TangentSolver;
 

include/fesa/analysis/linear_frequency_procedure.h

@@ -6,13 +6,23 @@
 namespace fesa {
 
 class Domain;
+class EigenSolver;
 
 /// @brief Executes the supported linear MITC4 frequency procedure.
 class LinearFrequencyProcedureExecutor final {
  public:
+  /// @brief Preserves default FEAST construction for existing callers.
+  LinearFrequencyProcedureExecutor() = default;
+
+  /// @brief Borrows a solver that must outlive this executor and its calls.
+  explicit LinearFrequencyProcedureExecutor(const EigenSolver& solver) : solver_(&solver) {}
+
   /// @brief Builds, solves, and validates one frequency modal candidate.
   /// @return Requested physical modes plus all-c validation evidence.
   Result<EigenAnalysisState> Execute(const Domain& domain) const;
+
+ private:
+  const EigenSolver* solver_{nullptr};
 };
 
 }  // namespace fesa

include/fesa/analysis/linear_static_execution_result.h

@@ -0,0 +1,19 @@
+#ifndef FESA_ANALYSIS_LINEAR_STATIC_EXECUTION_RESULT_H_
+#define FESA_ANALYSIS_LINEAR_STATIC_EXECUTION_RESULT_H_
+
+#include <vector>
+
+#include "fesa/analysis/analysis_state.h"
+#include "fesa/core/diagnostic.h"
+
+namespace fesa {
+
+/// @brief Stores a completed linear-static calculation before result writing.
+struct LinearStaticExecutionResult {
+  AnalysisState state;
+  std::vector<Diagnostic> diagnostics;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_LINEAR_STATIC_EXECUTION_RESULT_H_

include/fesa/analysis/linear_static_procedure.h

@@ -1,10 +1,13 @@
 #ifndef FESA_ANALYSIS_LINEAR_STATIC_PROCEDURE_H_
 #define FESA_ANALYSIS_LINEAR_STATIC_PROCEDURE_H_
 
-#include "fesa/analysis/prepared_analysis.h"
+#include "fesa/analysis/linear_static_execution_result.h"
+#include "fesa/core/status.h"
 
 namespace fesa {
 
+class Domain;
+
 class LinearSolver;
 class ParallelFor;
 

include/fesa/analysis/nonlinear_static_execution_result.h

@@ -0,0 +1,20 @@
+#ifndef FESA_ANALYSIS_NONLINEAR_STATIC_EXECUTION_RESULT_H_
+#define FESA_ANALYSIS_NONLINEAR_STATIC_EXECUTION_RESULT_H_
+
+#include <vector>
+
+#include "fesa/analysis/nonlinear_analysis_state.h"
+#include "fesa/core/diagnostic.h"
+
+namespace fesa {
+
+/// @brief Stores a completed nonlinear-static calculation before result
+/// writing.
+struct NonlinearStaticExecutionResult {
+  NonlinearAnalysisState state;
+  std::vector<Diagnostic> diagnostics;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_NONLINEAR_STATIC_EXECUTION_RESULT_H_

include/fesa/analysis/nonlinear_static_procedure.h

@@ -1,10 +1,13 @@
 #ifndef FESA_ANALYSIS_NONLINEAR_STATIC_PROCEDURE_H_
 #define FESA_ANALYSIS_NONLINEAR_STATIC_PROCEDURE_H_
 
-#include "fesa/analysis/prepared_analysis.h"
+#include "fesa/analysis/nonlinear_static_execution_result.h"
+#include "fesa/core/status.h"
 
 namespace fesa {
 
+class Domain;
+
 class NewtonIterationLogWriter;
 class ParallelFor;
 class TangentSolver;

include/fesa/analysis/prepared_analysis.h

@@ -2,23 +2,21 @@
 #define FESA_ANALYSIS_PREPARED_ANALYSIS_H_
 
 #include <filesystem>
-#include <variant>
+#include <memory>
 #include <vector>
 
-#include "fesa/analysis/analysis_state.h"
-#include "fesa/analysis/dynamic_analysis_state.h"
-#include "fesa/analysis/eigen_analysis_state.h"
-#include "fesa/analysis/nonlinear_analysis_state.h"
-#include "fesa/analysis/solid_frequency_state.h"
-#include "fesa/analysis/solid_hht_dynamic_procedure.h"
-#include "fesa/analysis/solid_static_procedure.h"
-#include "fesa/analysis/transient_heat_procedure.h"
+#include "fesa/analysis/analysis_procedure.h"
+#include "fesa/analysis/prepared_analysis_outcome.h"
 #include "fesa/core/diagnostic.h"
 #include "fesa/core/status.h"
 #include "fesa/model/domain.h"
 
 namespace fesa {
 
+class ParallelFor;
+class LinearSolver;
+class TangentSolver;
+class EigenSolver;
 class LinearStaticProcedureExecutor;
 class LinearFrequencyProcedureExecutor;
 class EigenResultsWriter;
@@ -31,6 +29,9 @@ class DynamicResultsWriter;
 class ThermalResultsWriter;
 class SolidResultsWriter;
 class SolidFrequencyProcedureExecutor;
+class SolidStaticProcedureExecutor;
+class SolidHhtDynamicProcedureExecutor;
+class TransientHeatProcedureExecutor;
 struct DerivedOutputPaths;
 
 /// @brief Owns one parsed and semantically mapped analysis input.
@@ -46,30 +47,16 @@ struct PreparedAnalysisInput {
 Result<PreparedAnalysisInput> PrepareAnalysisInput(
     const std::filesystem::path& input_path);
 
-/// @brief Stores a completed linear-static calculation before result writing.
-struct LinearStaticExecutionResult {
-  AnalysisState state;
-  std::vector<Diagnostic> diagnostics;
-};
+/// @brief Creates exactly one selected family with caller-owned adapters.
+/// @note Domain and adapters remain alive and unmoved throughout execution.
+Result<std::unique_ptr<AnalysisProcedure>> CreateAnalysisProcedure(
+    const Domain &domain, const ParallelFor &parallel_for,
+    LinearSolver &linear_solver, TangentSolver &tangent_solver,
+    const EigenSolver &eigen_solver, NewtonIterationLogWriter &log);
 
-/// @brief Stores a completed nonlinear-static calculation before result
-/// writing.
-struct NonlinearStaticExecutionResult {
-  NonlinearAnalysisState state;
-  std::vector<Diagnostic> diagnostics;
-};
-
-/// @brief Stores a complete HHT history before atomic result finalization.
-struct DynamicExecutionResult {
-  DynamicAnalysisState state;
-  std::vector<Diagnostic> diagnostics;
-};
-
-using PreparedAnalysisOutcome =
-    std::variant<LinearStaticExecutionResult, NonlinearStaticExecutionResult,
-                 EigenAnalysisState, DynamicExecutionResult,
-                 ThermalExecutionResult, SolidStaticExecutionResult,
-                 SolidFrequencyState, SolidDynamicExecutionResult>;
+/// @brief Executes a caller-selected procedure through the common interface.
+Result<PreparedAnalysisOutcome>
+ExecutePreparedAnalysis(const Domain &domain, AnalysisProcedure &procedure);
 
 /// @brief Selects the approved procedure from a prepared Domain.
 /// @pre The executors and log outlive this call.

include/fesa/analysis/prepared_analysis_outcome.h

@@ -0,0 +1,26 @@
+#ifndef FESA_ANALYSIS_PREPARED_ANALYSIS_OUTCOME_H_
+#define FESA_ANALYSIS_PREPARED_ANALYSIS_OUTCOME_H_
+
+#include <variant>
+
+#include "fesa/analysis/dynamic_execution_result.h"
+#include "fesa/analysis/eigen_analysis_state.h"
+#include "fesa/analysis/linear_static_execution_result.h"
+#include "fesa/analysis/nonlinear_static_execution_result.h"
+#include "fesa/analysis/solid_dynamic_execution_result.h"
+#include "fesa/analysis/solid_frequency_state.h"
+#include "fesa/analysis/solid_static_execution_result.h"
+#include "fesa/analysis/thermal_execution_result.h"
+
+namespace fesa {
+
+/// @brief Owns a completed procedure result before result-file finalization.
+using PreparedAnalysisOutcome =
+    std::variant<LinearStaticExecutionResult, NonlinearStaticExecutionResult,
+                 EigenAnalysisState, DynamicExecutionResult,
+                 ThermalExecutionResult, SolidStaticExecutionResult,
+                 SolidFrequencyState, SolidDynamicExecutionResult>;
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_PREPARED_ANALYSIS_OUTCOME_H_

include/fesa/analysis/solid_dynamic_execution_result.h

@@ -0,0 +1,17 @@
+#ifndef FESA_ANALYSIS_SOLID_DYNAMIC_EXECUTION_RESULT_H_
+#define FESA_ANALYSIS_SOLID_DYNAMIC_EXECUTION_RESULT_H_
+
+#include "fesa/analysis/solid_dynamic_analysis_state.h"
+#include "fesa/fem/dof_manager.h"
+
+namespace fesa {
+
+/// @brief Owns the validated 3N dynamic result independently of serialization.
+struct SolidDynamicExecutionResult {
+  DofManager dofs;
+  SolidDynamicAnalysisState state;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_SOLID_DYNAMIC_EXECUTION_RESULT_H_

include/fesa/analysis/solid_frequency_procedure.h

@@ -5,14 +5,24 @@
 
 namespace fesa {
 class Domain;
+class EigenSolver;
 /// @brief Executes unloaded reference-state C3D8 generalized frequency
 /// analysis.
 class SolidFrequencyProcedureExecutor final {
  public:
+  /// @brief Preserves default FEAST construction for existing callers.
+  SolidFrequencyProcedureExecutor() = default;
+
+  /// @brief Borrows a solver that must outlive this executor and its calls.
+  explicit SolidFrequencyProcedureExecutor(const EigenSolver& solver) : solver_(&solver) {}
+
   /// @brief Returns lowest requested modes after validating every returned
   /// pair.
   /// @note Domain is immutable and must remain alive during execution.
   Result<SolidFrequencyState> Execute(const Domain& domain) const;
+
+ private:
+  const EigenSolver* solver_{nullptr};
 };
 }  // namespace fesa
 #endif  // FESA_ANALYSIS_SOLID_FREQUENCY_PROCEDURE_H_

include/fesa/analysis/solid_frequency_state.h

@@ -8,7 +8,7 @@
 #include <vector>
 
 #include "fesa/math/matrix.h"
-#include "fesa/solvers/eigen/mkl_feast_eigen_solver.h"
+#include "fesa/solvers/eigen/eigen_solver.h"
 
 namespace fesa {
 /// @brief Identifies a source-ordered physical Solid eigenmode.

include/fesa/analysis/solid_hht_dynamic_procedure.h

@@ -1,19 +1,13 @@
 #ifndef FESA_ANALYSIS_SOLID_HHT_DYNAMIC_PROCEDURE_H_
 #define FESA_ANALYSIS_SOLID_HHT_DYNAMIC_PROCEDURE_H_
 
-#include "fesa/analysis/solid_dynamic_analysis_state.h"
+#include "fesa/analysis/solid_dynamic_execution_result.h"
 
 namespace fesa {
 class LinearSolver;
 class ParallelFor;
 class TangentSolver;
 
-/// @brief Owns the validated 3N dynamic result independently of serialization.
-struct SolidDynamicExecutionResult {
-  DofManager dofs;
-  SolidDynamicAnalysisState state;
-};
-
 /// @brief Integrates linear or TL Solid mechanics with constant consistent
 /// mass.
 class SolidHhtDynamicProcedureExecutor {

include/fesa/analysis/solid_static_execution_result.h

@@ -0,0 +1,19 @@
+#ifndef FESA_ANALYSIS_SOLID_STATIC_EXECUTION_RESULT_H_
+#define FESA_ANALYSIS_SOLID_STATIC_EXECUTION_RESULT_H_
+
+#include <vector>
+
+#include "fesa/analysis/solid_static_state.h"
+#include "fesa/core/diagnostic.h"
+
+namespace fesa {
+
+/// @brief Owns successful static frames and sorted model diagnostics.
+struct SolidStaticExecutionResult {
+  SolidStaticState state;
+  std::vector<Diagnostic> diagnostics;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_SOLID_STATIC_EXECUTION_RESULT_H_

include/fesa/analysis/solid_static_procedure.h

@@ -1,19 +1,13 @@
 #ifndef FESA_ANALYSIS_SOLID_STATIC_PROCEDURE_H_
 #define FESA_ANALYSIS_SOLID_STATIC_PROCEDURE_H_
 
-#include "fesa/analysis/solid_static_state.h"
+#include "fesa/analysis/solid_static_execution_result.h"
 
 namespace fesa {
 class LinearSolver;
 class ParallelFor;
 class TangentSolver;
 
-/// @brief Owns successful static frames and sorted model diagnostics.
-struct SolidStaticExecutionResult {
-  SolidStaticState state;
-  std::vector<Diagnostic> diagnostics;
-};
-
 /// @brief Executes linear K0 or fixed-factor TL StVK static analysis.
 class SolidStaticProcedureExecutor {
  public:

include/fesa/analysis/solid_static_state.h

@@ -99,7 +99,7 @@ class SolidStaticState {
       const noexcept;
 
  private:
-  friend class SolidStaticProcedureExecutor;
+  friend class SolidStaticCore;
   bool initialized_{false};
   bool nonlinear_{false};
   std::vector<SolidIntegrationPointRow> reference_points_;

include/fesa/analysis/thermal_analysis_state.h

@@ -6,11 +6,15 @@
 #include <vector>
 
 #include "fesa/analysis/thermal_time_grid.h"
-#include "fesa/assembly/thermal_assembler.h"
+#include "fesa/core/status.h"
 #include "fesa/results/thermal_result_records.h"
 
 namespace fesa {
 
+class AnalysisModel;
+class DofManager;
+class ThermalAssembly;
+
 /// @brief Owns the immutable thermal result inventory and accepted history.
 /// @note No Domain/model/assembly references survive Create; state may outlive
 /// them. Numerical equilibrium and energy checks belong to the procedure before

include/fesa/analysis/thermal_execution_result.h

@@ -0,0 +1,19 @@
+#ifndef FESA_ANALYSIS_THERMAL_EXECUTION_RESULT_H_
+#define FESA_ANALYSIS_THERMAL_EXECUTION_RESULT_H_
+
+#include <vector>
+
+#include "fesa/analysis/thermal_analysis_state.h"
+#include "fesa/core/diagnostic.h"
+
+namespace fesa {
+
+/// @brief Owns complete thermal history before any result output is opened.
+struct ThermalExecutionResult {
+  ThermalAnalysisState state;
+  std::vector<Diagnostic> diagnostics;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_THERMAL_EXECUTION_RESULT_H_

include/fesa/analysis/transient_heat_procedure.h

@@ -1,21 +1,14 @@
 #ifndef FESA_ANALYSIS_TRANSIENT_HEAT_PROCEDURE_H_
 #define FESA_ANALYSIS_TRANSIENT_HEAT_PROCEDURE_H_
 
-#include <vector>
-
-#include "fesa/analysis/thermal_analysis_state.h"
+#include "fesa/analysis/thermal_execution_result.h"
 #include "fesa/core/status.h"
 
 namespace fesa {
+class Domain;
 class LinearSolver;
 class ParallelFor;
 
-/// @brief Owns complete thermal history before any result output is opened.
-struct ThermalExecutionResult {
-  ThermalAnalysisState state;
-  std::vector<Diagnostic> diagnostics;
-};
-
 /// @brief Executes fixed-increment backward Euler with checked thermal
 /// recovery.
 class TransientHeatProcedureExecutor final {

include/fesa/assembly/load_assembler.h

@@ -30,7 +30,8 @@ class LoadAssembler {
                                               double step_time = 0.0);
 
   /// @brief Forms Ff-Kfc*dc in stable free/constrained order.
-  /// @note This operation neither factorizes nor invokes a solver.
+  /// @note Compatibility facade delegates to EssentialConstraintPolicy; this
+  /// operation neither factorizes nor invokes a solver.
   static Result<Vector> EffectiveFreeRhs(const Vector& full_load,
                                          const SparseMatrix& kfc,
                                          const Vector& prescribed_values,

include/fesa/assembly/thermal_assembler.h

@@ -2,10 +2,12 @@
 #define FESA_ASSEMBLY_THERMAL_ASSEMBLER_H_
 
 #include <array>
+#include <memory>
 #include <vector>
 
 #include "fesa/analysis/analysis_model.h"
 #include "fesa/assembly/parallel_for.h"
+#include "fesa/elements/element_capabilities.h"
 #include "fesa/elements/thermal_shell.h"
 #include "fesa/fem/dof_manager.h"
 #include "fesa/math/sparse_matrix.h"
@@ -50,6 +52,8 @@ class ThermalAssembly final {
   const std::vector<EntityIndex>& ElementOrder() const noexcept;
   /// @brief Returns checked kernels in stable active element order.
   const std::vector<ThermalShell>& Kernels() const noexcept;
+  /// @brief Returns typed views bound after the final kernel buffer is placed.
+  const std::vector<std::unique_ptr<ThermalElement>>& Elements() const noexcept;
   /// @brief Returns node-major twenty-entry full DOF scatters in kernel order.
   const std::vector<std::array<std::size_t, 20>>& Scatters() const noexcept;
   /// @brief Checks source Domain identity and the complete supplied equation
@@ -79,7 +83,10 @@ class ThermalAssembly final {
   SparseMatrix capacity_error_;
   Vector input_error_;
   std::vector<EntityIndex> element_order_;
+  // Never resized after construction. Moving the owning vector transfers its
+  // buffer, so bound references survive ThermalAssembly moves.
   std::vector<ThermalShell> kernels_;
+  std::vector<std::unique_ptr<ThermalElement>> elements_;
   std::vector<std::array<std::size_t, 20>> scatters_;
 };
 

include/fesa/constraints/essential_constraint_policy.h

@@ -24,6 +24,16 @@ class EssentialConstraintPolicy {
   Result<PartitionedStiffness> Partition(const SparseMatrix& full_stiffness,
                                          const DofManager& dof_manager) const;
 
+  /// @brief Forms Ff-Kfc*dc in stable free/constrained order.
+  /// @return A finite RHS candidate or the established load diagnostic.
+  /// @note Preserves independent CSR products and ordered row reductions;
+  /// no factorization or solver operation is performed. Inputs are borrowed
+  /// only for this call and remain unchanged on failure.
+  Result<Vector> EffectiveFreeRhs(const Vector& full_load,
+                                   const SparseMatrix& kfc,
+                                   const Vector& prescribed_values,
+                                   const DofManager& dofs) const;
+
   /// @brief Gathers a full vector in stable free-equation order.
   Vector GatherFree(const Vector& full_values,
                     const DofManager& dof_manager) const;

include/fesa/constraints/prescribed_displacement.h

@@ -5,7 +5,7 @@
 
 #include "fesa/constraints/boundary_condition.h"
 #include "fesa/core/diagnostic.h"
-#include "fesa/elements/element.h"
+#include "fesa/elements/element_dof_layout.h"
 #include "fesa/model/source_target_resolver.h"
 
 namespace fesa {

include/fesa/core/ascii.h

@@ -2,6 +2,7 @@
 #define FESA_CORE_ASCII_H_
 
 #include <cstdint>
+#include <string>
 #include <string_view>
 
 #include "fesa/core/status.h"
@@ -12,6 +13,11 @@ namespace fesa {
 /// @return The lowercase ASCII byte, or the input byte when it is not A-Z.
 char AsciiLower(char value) noexcept;
 
+/// @brief Returns an uppercase ASCII copy without changing other source bytes.
+/// @note Embedded nulls and non-ASCII bytes are preserved without locale
+/// folding.
+std::string AsciiUppercase(std::string value);
+
 /// @brief Compares two byte strings with ASCII-only case folding.
 /// @return True when the strings have equal length and equal ASCII-folded
 /// bytes.

include/fesa/core/source_identity.h

@@ -24,6 +24,14 @@ struct SourceEntityId {
   std::string source_label_text;
 };
 
+/// @brief Compares all preserved source fields without canonicalizing spelling.
+inline bool SourceIdentityEquals(const SourceEntityId& left,
+                                const SourceEntityId& right) noexcept {
+  return left.instance_name == right.instance_name &&
+         left.source_label == right.source_label &&
+         left.source_label_text == right.source_label_text;
+}
+
 }  // namespace fesa
 
 #endif  // FESA_CORE_SOURCE_IDENTITY_H_

include/fesa/core/status.h

@@ -98,11 +98,11 @@ class Result {
   struct FailureTag {};
 
   /// @brief Constructs the successful value alternative.
-  Result(SuccessTag, T value)
+  Result(SuccessTag, T&& value)
       : value_{std::move(value)}, status_{Status::Ok()} {}
 
   /// @brief Constructs the failed status alternative.
-  Result(FailureTag, Status status)
+  Result(FailureTag, Status&& status)
       : value_{std::nullopt}, status_{std::move(status)} {}
 
   std::optional<T> value_;

include/fesa/elements/element.h

@@ -1,13 +1,11 @@
 #ifndef FESA_ELEMENTS_ELEMENT_H_
 #define FESA_ELEMENTS_ELEMENT_H_
 
-#include <cstdint>
-#include <functional>
 #include <variant>
 #include <vector>
 
-#include "fesa/core/source_identity.h"
 #include "fesa/core/status.h"
+#include "fesa/elements/element_dof_layout.h"
 #include "fesa/math/matrix.h"
 #include "fesa/math/vector.h"
 #include "fesa/results/result_records.h"
@@ -15,23 +13,6 @@
 
 namespace fesa {
 
-/// @brief Identifies one component in the stable six-DOF node layout.
-enum class DofComponent : std::uint8_t {
-  kUx,
-  kUy,
-  kUz,
-  kUrx,
-  kUry,
-  kUrz,
-};
-
-/// @brief Describes one runtime element's stable node and component order.
-struct ElementDofLayout {
-  SourceEntityId source_id;
-  std::vector<EntityIndex> node_indices;
-  std::vector<DofComponent> components_per_node;
-};
-
 /// @brief Carries one element-local stiffness in its declared DOF order.
 struct ElementStiffnessContribution {
   ElementDofLayout layout;
@@ -78,10 +59,6 @@ class Element {
       const Vector& element_displacement) const = 0;
 };
 
-/// @brief Provides non-owning runtime elements in stable owner order.
-/// @note Every referenced element must outlive this view.
-using ElementView = std::vector<std::reference_wrapper<const Element>>;
-
 }  // namespace fesa
 
 #endif  // FESA_ELEMENTS_ELEMENT_H_

include/fesa/elements/element_capabilities.h

@@ -0,0 +1,200 @@
+#ifndef FESA_ELEMENTS_ELEMENT_CAPABILITIES_H_
+#define FESA_ELEMENTS_ELEMENT_CAPABILITIES_H_
+
+#include <array>
+#include <cstddef>
+
+#include "fesa/elements/element.h"
+#include "fesa/elements/thermal_element_layout.h"
+#include "fesa/math/vector3.h"
+
+namespace fesa {
+
+class Hex8Element;
+class Mitc4Shell;
+class NonlinearMitc4Shell;
+class NonlinearMitc4Inertia;
+class ThermalShell;
+struct Hex8Response;
+struct Hex8HighLowResponse;
+struct Mitc4Stiffness;
+struct Mitc4Mass;
+struct NonlinearMitc4TrialDofs;
+struct NonlinearMitc4InternalEquilibrium;
+struct NonlinearMitc4ExternalDrillingConstraint;
+struct NonlinearMitc4InertiaEvaluation;
+struct ThermalShellRecovery;
+
+/// @brief Evaluates immutable shell trials; accepted history belongs to the procedure.
+class ShellTrialElement {
+ public:
+  virtual ~ShellTrialElement() = default;
+  /// @brief Returns stable source-local node/component order, never equations.
+  virtual const ElementDofLayout& DofLayout() const noexcept = 0;
+  /// @brief Returns the complete force/tangent/recovery at a fixed-global trial.
+  /// @param coordinate_direction Optional 24-vector for D2(f_int)[v,v].
+  /// @note Failure preserves the kernel, caller inputs and earlier responses.
+  virtual Result<NonlinearMitc4InternalEquilibrium> EvaluateTrial(
+      const NonlinearMitc4TrialDofs& trial,
+      const Vector* coordinate_direction = nullptr) const = 0;
+  /// @copydoc NonlinearMitc4Shell::EvaluateExternalDrillingConstraint
+  virtual Result<NonlinearMitc4ExternalDrillingConstraint>
+  EvaluateExternalDrillingConstraint(
+      std::size_t node, const Vector3& phi, const Vector3& phi_dot,
+      const Vector3& force, const Vector3& force_rate,
+      const Vector3& force_acceleration) const = 0;
+};
+
+/// @brief Borrows the same immutable shell kernel for every trial operation.
+/// @note The kernel must outlive this adapter and remain at its bound address.
+class Mitc4TrialAdapter final : public ShellTrialElement {
+ public:
+  Mitc4TrialAdapter(ElementDofLayout layout, const NonlinearMitc4Shell& kernel);
+  const ElementDofLayout& DofLayout() const noexcept override;
+  Result<NonlinearMitc4InternalEquilibrium> EvaluateTrial(
+      const NonlinearMitc4TrialDofs& trial,
+      const Vector* coordinate_direction = nullptr) const override;
+  Result<NonlinearMitc4ExternalDrillingConstraint>
+  EvaluateExternalDrillingConstraint(
+      std::size_t node, const Vector3& phi, const Vector3& phi_dot,
+      const Vector3& force, const Vector3& force_rate,
+      const Vector3& force_acceleration) const override;
+
+ private:
+  ElementDofLayout layout_;
+  const NonlinearMitc4Shell& kernel_;
+};
+
+/// @brief Keeps complete paired solid responses and reference mass typed.
+class SolidTrialElement : public Element {
+ public:
+  ~SolidTrialElement() override = default;
+  /// @copydoc Hex8Element::EvaluateLinear
+  virtual Result<Hex8Response> EvaluateLinear(const Vector& u) const = 0;
+  /// @copydoc Hex8Element::EvaluateNonlinear
+  virtual Result<Hex8Response> EvaluateNonlinear(const Vector& u) const = 0;
+  /// @copydoc Hex8Element::EvaluateLinearHighLow
+  virtual Result<Hex8HighLowResponse> EvaluateLinearHighLow(
+      const Vector& high, const Vector& low) const = 0;
+  /// @copydoc Hex8Element::EvaluateNonlinearHighLow
+  virtual Result<Hex8HighLowResponse> EvaluateNonlinearHighLow(
+      const Vector& high, const Vector& low) const = 0;
+  /// @copydoc Hex8Element::ComputeMass
+  virtual Result<ElementStiffnessContribution> ComputeMass() const = 0;
+  /// @brief Returns fixed Gauss weights used by the frequency mass bound.
+  virtual std::array<double, 8> ReferenceWeights() const noexcept = 0;
+};
+
+/// @brief Borrows one stable Hex8 kernel shared by all local operations.
+/// @note The kernel must outlive this adapter and remain at its bound address.
+class Hex8TrialAdapter final : public SolidTrialElement {
+ public:
+  explicit Hex8TrialAdapter(const Hex8Element& kernel);
+  const ElementDofLayout& DofLayout() const noexcept override;
+  Result<ElementStiffnessContribution> ComputeStiffness() const override;
+  Result<ElementResultBundle> Recover(const Vector& u) const override;
+  Result<Hex8Response> EvaluateLinear(const Vector& u) const override;
+  Result<Hex8Response> EvaluateNonlinear(const Vector& u) const override;
+  Result<Hex8HighLowResponse> EvaluateLinearHighLow(
+      const Vector& high, const Vector& low) const override;
+  Result<Hex8HighLowResponse> EvaluateNonlinearHighLow(
+      const Vector& high, const Vector& low) const override;
+  Result<ElementStiffnessContribution> ComputeMass() const override;
+  std::array<double, 8> ReferenceWeights() const noexcept override;
+
+ private:
+  const Hex8Element& kernel_;
+};
+
+/// @brief Returns the complete physical inertia response in fixed chart DOFs.
+class ShellInertiaElement {
+ public:
+  virtual ~ShellInertiaElement() = default;
+  virtual const ElementDofLayout& DofLayout() const noexcept = 0;
+  /// @copydoc NonlinearMitc4Inertia::Evaluate
+  virtual Result<NonlinearMitc4InertiaEvaluation> Evaluate(
+      const NonlinearMitc4TrialDofs& trial, const Vector& velocity24,
+      const Vector& physical_acceleration24) const = 0;
+};
+
+/// @brief Borrows immutable inertia geometry, never shared mutable scratch.
+/// @note The kernel must outlive this adapter and remain at its bound address.
+class Mitc4InertiaAdapter final : public ShellInertiaElement {
+ public:
+  Mitc4InertiaAdapter(ElementDofLayout layout,
+                      const NonlinearMitc4Inertia& kernel);
+  const ElementDofLayout& DofLayout() const noexcept override;
+  Result<NonlinearMitc4InertiaEvaluation> Evaluate(
+      const NonlinearMitc4TrialDofs& trial, const Vector& velocity24,
+      const Vector& physical_acceleration24) const override;
+
+ private:
+  ElementDofLayout layout_;
+  const NonlinearMitc4Inertia& kernel_;
+};
+
+/// @brief Keeps DS4 DOFs 11-15 and all four-by-six flux traces independent.
+class ThermalElement {
+ public:
+  virtual ~ThermalElement() = default;
+  /// @brief Returns node-major stations 11-15 and original source identity.
+  virtual const ThermalElementDofLayout& DofLayout() const noexcept = 0;
+  /// @copydoc ThermalShell::Conductivity
+  virtual const Matrix& Conductivity() const noexcept = 0;
+  /// @copydoc ThermalShell::Capacity
+  virtual const Matrix& Capacity() const noexcept = 0;
+  /// @copydoc ThermalShell::ConductivityError
+  virtual const Matrix& ConductivityError() const noexcept = 0;
+  /// @copydoc ThermalShell::CapacityError
+  virtual const Matrix& CapacityError() const noexcept = 0;
+  /// @copydoc ThermalShell::Recover
+  virtual Result<ThermalShellRecovery> Recover(
+      const std::array<double, 20>& temperature) const = 0;
+};
+
+/// @brief Borrows the same DS4 kernel for matrices, intervals and recovery.
+/// @note The kernel must outlive this adapter and remain at its bound address.
+class Ds4ThermalAdapter final : public ThermalElement {
+ public:
+  explicit Ds4ThermalAdapter(const ThermalShell& kernel);
+  const ThermalElementDofLayout& DofLayout() const noexcept override;
+  const Matrix& Conductivity() const noexcept override;
+  const Matrix& Capacity() const noexcept override;
+  const Matrix& ConductivityError() const noexcept override;
+  const Matrix& CapacityError() const noexcept override;
+  Result<ThermalShellRecovery> Recover(
+      const std::array<double, 20>& temperature) const override;
+
+ private:
+  ThermalElementDofLayout layout_;
+  const ThermalShell& kernel_;
+};
+
+/// @brief Supplies shell frequency operators with their distinct mass contract.
+class ShellReferenceElement : public Element {
+ public:
+  ~ShellReferenceElement() override = default;
+  /// @copydoc Mitc4Shell::Stiffness
+  virtual Result<Mitc4Stiffness> Stiffness() const = 0;
+  /// @copydoc Mitc4Shell::Mass
+  virtual Result<Mitc4Mass> Mass(double density) const = 0;
+};
+
+/// @brief Borrows the same linear MITC4 kernel for stiffness and recovery.
+/// @note The kernel must outlive this adapter and remain at its bound address.
+class Mitc4ReferenceAdapter final : public ShellReferenceElement {
+ public:
+  explicit Mitc4ReferenceAdapter(const Mitc4Shell& kernel);
+  const ElementDofLayout& DofLayout() const noexcept override;
+  Result<ElementStiffnessContribution> ComputeStiffness() const override;
+  Result<ElementResultBundle> Recover(const Vector& u) const override;
+  Result<Mitc4Stiffness> Stiffness() const override;
+  Result<Mitc4Mass> Mass(double density) const override;
+
+ private:
+  const Mitc4Shell& kernel_;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ELEMENTS_ELEMENT_CAPABILITIES_H_

include/fesa/elements/element_dof_layout.h

@@ -0,0 +1,38 @@
+#ifndef FESA_ELEMENTS_ELEMENT_DOF_LAYOUT_H_
+#define FESA_ELEMENTS_ELEMENT_DOF_LAYOUT_H_
+
+#include <cstdint>
+#include <functional>
+#include <vector>
+
+#include "fesa/core/source_identity.h"
+
+namespace fesa {
+
+/// @brief Identifies one component in the stable six-DOF node layout.
+enum class DofComponent : std::uint8_t {
+  kUx,
+  kUy,
+  kUz,
+  kUrx,
+  kUry,
+  kUrz,
+};
+
+/// @brief Describes one runtime element's stable node and component order.
+struct ElementDofLayout {
+  SourceEntityId source_id;
+  std::vector<EntityIndex> node_indices;
+  std::vector<DofComponent> components_per_node;
+};
+
+class Element;
+
+/// @brief Provides non-owning runtime elements in stable owner order.
+/// @note Every referenced element must outlive this view.
+using ElementView = std::vector<std::reference_wrapper<const Element>>;
+
+
+}  // namespace fesa
+
+#endif  // FESA_ELEMENTS_ELEMENT_DOF_LAYOUT_H_

include/fesa/elements/element_factory.h

@@ -5,6 +5,7 @@
 
 #include "fesa/core/status.h"
 #include "fesa/elements/element.h"
+#include "fesa/elements/element_capabilities.h"
 
 namespace fesa {
 
@@ -21,6 +22,14 @@ class ElementFactory {
   Result<std::unique_ptr<Element>> Create(const ElementDefinition& definition,
                                           const Domain& domain) const;
 
+  /// @brief Binds a typed view of an existing stable runtime kernel.
+  /// @note Returns null for a different family. The kernel must outlive the
+  /// returned adapter and remain at its address; no second kernel is created.
+  std::unique_ptr<SolidTrialElement> BindSolidTrial(const Element& kernel) const;
+  /// @copydoc BindSolidTrial
+  std::unique_ptr<ShellReferenceElement> BindShellReference(
+      const Element& kernel) const;
+
  private:
   /// @brief Creates one checked B33 runtime candidate.
   Result<std::unique_ptr<Element>> CreateBeam(

include/fesa/elements/euler_beam_3d.h

@@ -4,12 +4,11 @@
 #include <array>
 #include <cstddef>
 #include <string>
-#include <string_view>
 #include <vector>
 
 #include "fesa/core/status.h"
 #include "fesa/elements/element.h"
-#include "fesa/elements/element_definition.h"
+#include "fesa/elements/euler_beam_3d_definition.h"
 #include "fesa/materials/isotropic_linear_elastic_material.h"
 #include "fesa/math/matrix.h"
 #include "fesa/math/vector.h"
@@ -17,40 +16,8 @@
 
 namespace fesa {
 
-class Domain;
 struct Node;
 
-/// @brief Defines one two-node B33 semantic element.
-class EulerBeam3DDefinition final : public ElementDefinition {
- public:
-  /// @brief Constructs a parser-validated semantic definition.
-  EulerBeam3DDefinition(SourceEntityId source_id,
-                        std::array<EntityIndex, 2> node_indices,
-                        EntityIndex material_index, EntityIndex section_index,
-                        SourceLocation location);
-
-  ElementDefinitionKind Kind() const noexcept override;
-  const SourceEntityId& SourceId() const noexcept override;
-  std::string_view SourceElementType() const noexcept override;
-  const std::vector<EntityIndex>& NodeIndices() const noexcept override;
-  EntityIndex MaterialIndex() const noexcept override;
-  EntityIndex PropertyIndex() const noexcept override;
-
-  SourceEntityId source_id;
-  std::array<EntityIndex, 2> node_indices;
-  EntityIndex material_index;
-  EntityIndex section_index;
-  SourceLocation location;
-
- private:
-  friend class Domain;
-
-  /// @brief Synchronizes the base view after parser-candidate construction.
-  void SynchronizeNodeIndices();
-
-  std::vector<EntityIndex> node_indices_view_;
-};
-
 /// @brief Stores constant line-load components in the beam local frame.
 struct ConstantLocalLineLoad {
   double px;

include/fesa/elements/euler_beam_3d_definition.h

@@ -0,0 +1,48 @@
+#ifndef FESA_ELEMENTS_EULER_BEAM_3D_DEFINITION_H_
+#define FESA_ELEMENTS_EULER_BEAM_3D_DEFINITION_H_
+
+#include <array>
+#include <string_view>
+#include <vector>
+
+#include "fesa/elements/element_definition.h"
+
+namespace fesa {
+
+class Domain;
+
+/// @brief Defines one two-node B33 semantic element.
+class EulerBeam3DDefinition final : public ElementDefinition {
+ public:
+  /// @brief Constructs a parser-validated semantic definition.
+  EulerBeam3DDefinition(SourceEntityId source_id,
+                        std::array<EntityIndex, 2> node_indices,
+                        EntityIndex material_index, EntityIndex section_index,
+                        SourceLocation location);
+
+  ElementDefinitionKind Kind() const noexcept override;
+  const SourceEntityId& SourceId() const noexcept override;
+  std::string_view SourceElementType() const noexcept override;
+  const std::vector<EntityIndex>& NodeIndices() const noexcept override;
+  EntityIndex MaterialIndex() const noexcept override;
+  EntityIndex PropertyIndex() const noexcept override;
+
+  SourceEntityId source_id;
+  std::array<EntityIndex, 2> node_indices;
+  EntityIndex material_index;
+  EntityIndex section_index;
+  SourceLocation location;
+
+ private:
+  friend class Domain;
+
+  /// @brief Synchronizes the base view after parser-candidate construction.
+  void SynchronizeNodeIndices();
+
+  std::vector<EntityIndex> node_indices_view_;
+};
+
+
+}  // namespace fesa
+
+#endif  // FESA_ELEMENTS_EULER_BEAM_3D_DEFINITION_H_

include/fesa/elements/finite_rotation.h

@@ -33,11 +33,13 @@ Matrix ExpSkew(const Vector3& phi);
 /// @pre phi is finite and lies inside the approved principal chart.
 Matrix LeftJacobianSO3(const Vector3& phi);
 
-/// @brief Computes the inverse transpose of the SO(3) left Jacobian.
-/// @param phi Fixed-global rotation coordinate in radians.
-/// @return The 3-by-3 inverse-transpose left Jacobian.
+/// @brief Solves J(phi)^T * moment = generalized for a spatial moment.
+/// @param phi Fixed-global principal-chart rotation coordinate in radians.
+/// @param generalized Work-conjugate moment in fixed-global chart coordinates.
+/// @return A finite spatial moment in the same force-length units, or failure.
 /// @pre phi is finite and lies inside the approved principal chart.
-Matrix InverseTransposeLeftJacobianSO3(const Vector3& phi);
+/// @note Inputs remain unchanged; no inverse Jacobian is constructed.
+Result<Vector3> SpatialMomentSO3(const Vector3& phi, const Vector3& generalized);
 
 /// @brief Builds a checked finite-rotation state from its reference frame.
 /// @param phi Fixed-global principal-chart rotation coordinate in radians.

include/fesa/elements/mitc4_shell.h

@@ -3,12 +3,11 @@
 
 #include <array>
 #include <string>
-#include <string_view>
 #include <vector>
 
 #include "fesa/core/status.h"
 #include "fesa/elements/element.h"
-#include "fesa/elements/element_definition.h"
+#include "fesa/elements/mitc4_shell_definition.h"
 #include "fesa/materials/isotropic_linear_elastic_material.h"
 #include "fesa/math/matrix.h"
 #include "fesa/math/vector.h"
@@ -17,52 +16,8 @@
 
 namespace fesa {
 
-class Domain;
 struct Node;
 
-/// @brief Preserves the source shell type independently of formulation.
-enum class ShellSourceElementType { kS4, kS4r };
-
-/// @brief Names the internal shell formulation selected by S4 and S4R.
-inline constexpr std::string_view kMitc4InternalFormulation{"FESA-MITC4"};
-
-/// @brief Defines one four-node S4/S4R semantic element.
-class Mitc4ShellDefinition final : public ElementDefinition {
- public:
-  /// @brief Constructs a parser-validated semantic definition.
-  Mitc4ShellDefinition(SourceEntityId source_id,
-                       ShellSourceElementType source_type,
-                       std::array<EntityIndex, 4> node_indices,
-                       EntityIndex material_index, EntityIndex section_index,
-                       SourceLocation location);
-
-  ElementDefinitionKind Kind() const noexcept override;
-  const SourceEntityId& SourceId() const noexcept override;
-  std::string_view SourceElementType() const noexcept override;
-  const std::vector<EntityIndex>& NodeIndices() const noexcept override;
-  EntityIndex MaterialIndex() const noexcept override;
-  EntityIndex PropertyIndex() const noexcept override;
-
-  SourceEntityId source_id;
-  ShellSourceElementType source_type;
-  std::array<EntityIndex, 4> node_indices;
-  EntityIndex material_index;
-  EntityIndex section_index;
-  SourceLocation location;
-
- private:
-  friend class Domain;
-
-  /// @brief Rebinds a shell-local section index to the unified property view.
-  void SetPropertyIndex(EntityIndex property_index) noexcept;
-
-  /// @brief Synchronizes the base view after parser-candidate construction.
-  void SynchronizeNodeIndices();
-
-  EntityIndex property_index_;
-  std::vector<EntityIndex> node_indices_view_;
-};
-
 /// @brief Stores bilinear shape values and natural-coordinate derivatives.
 struct Mitc4ShapeFunctions {
   std::array<double, 4> values;
@@ -213,11 +168,10 @@ class Mitc4Shell final : public Element {
   void BindRuntime(ElementDofLayout layout, EntityIndex element_index,
                    SourceLocation location);
 
-  /// @brief Stores covariant, reciprocal, frame, and Jacobian data at one
+  /// @brief Stores covariant, frame, and Jacobian data at one
   /// point.
   struct GeometryData {
     std::array<Vector3, 3> covariant;
-    std::array<Vector3, 3> reciprocal;
     Mitc4LocalFrame frame;
     double jacobian;
   };

include/fesa/elements/mitc4_shell_definition.h

@@ -0,0 +1,60 @@
+#ifndef FESA_ELEMENTS_MITC4_SHELL_DEFINITION_H_
+#define FESA_ELEMENTS_MITC4_SHELL_DEFINITION_H_
+
+#include <array>
+#include <string_view>
+#include <vector>
+
+#include "fesa/elements/element_definition.h"
+
+namespace fesa {
+
+class Domain;
+
+/// @brief Preserves the source shell type independently of formulation.
+enum class ShellSourceElementType { kS4, kS4r };
+
+/// @brief Names the internal shell formulation selected by S4 and S4R.
+inline constexpr std::string_view kMitc4InternalFormulation{"FESA-MITC4"};
+
+/// @brief Defines one four-node S4/S4R semantic element.
+class Mitc4ShellDefinition final : public ElementDefinition {
+ public:
+  /// @brief Constructs a parser-validated semantic definition.
+  Mitc4ShellDefinition(SourceEntityId source_id,
+                       ShellSourceElementType source_type,
+                       std::array<EntityIndex, 4> node_indices,
+                       EntityIndex material_index, EntityIndex section_index,
+                       SourceLocation location);
+
+  ElementDefinitionKind Kind() const noexcept override;
+  const SourceEntityId& SourceId() const noexcept override;
+  std::string_view SourceElementType() const noexcept override;
+  const std::vector<EntityIndex>& NodeIndices() const noexcept override;
+  EntityIndex MaterialIndex() const noexcept override;
+  EntityIndex PropertyIndex() const noexcept override;
+
+  SourceEntityId source_id;
+  ShellSourceElementType source_type;
+  std::array<EntityIndex, 4> node_indices;
+  EntityIndex material_index;
+  EntityIndex section_index;
+  SourceLocation location;
+
+ private:
+  friend class Domain;
+
+  /// @brief Rebinds a shell-local section index to the unified property view.
+  void SetPropertyIndex(EntityIndex property_index) noexcept;
+
+  /// @brief Synchronizes the base view after parser-candidate construction.
+  void SynchronizeNodeIndices();
+
+  EntityIndex property_index_;
+  std::vector<EntityIndex> node_indices_view_;
+};
+
+
+}  // namespace fesa
+
+#endif  // FESA_ELEMENTS_MITC4_SHELL_DEFINITION_H_

include/fesa/elements/thermal_dof_component.h

@@ -0,0 +1,20 @@
+#ifndef FESA_ELEMENTS_THERMAL_DOF_COMPONENT_H_
+#define FESA_ELEMENTS_THERMAL_DOF_COMPONENT_H_
+
+
+namespace fesa {
+
+/// @brief Identifies the fixed bottom-to-top thermal station source DOFs.
+/// @note This is separate from the six-component structural DofComponent.
+enum class ThermalDofComponent : int {
+  kBottom = 11,
+  kLower = 12,
+  kMiddle = 13,
+  kUpper = 14,
+  kTop = 15
+};
+
+
+}  // namespace fesa
+
+#endif  // FESA_ELEMENTS_THERMAL_DOF_COMPONENT_H_

include/fesa/elements/thermal_element_layout.h

@@ -3,7 +3,8 @@
 
 #include <array>
 
-#include "fesa/model/model_types.h"
+#include "fesa/core/source_identity.h"
+#include "fesa/elements/thermal_dof_component.h"
 
 namespace fesa {
 

include/fesa/fem/dof_manager.h

@@ -6,25 +6,20 @@
 #include <optional>
 #include <vector>
 
-#include "fesa/analysis/analysis_model.h"
 #include "fesa/constraints/boundary_condition.h"
-#include "fesa/elements/element.h"
+#include "fesa/elements/element_dof_layout.h"
 #include "fesa/elements/thermal_element_layout.h"
+#include "fesa/math/sparse_pattern.h"
 #include "fesa/math/vector.h"
 
 namespace fesa {
 
+class AnalysisModel;
 class DofManagerTestAccess;
 
 /// @brief Distinguishes six-component, Solid translation, and thermal maps.
 enum class DofProfile { kStructural, kThermal, kSolidStructural };
 
-/// @brief Stores the stable full-space CSR pattern.
-struct SparsePattern {
-  std::vector<std::size_t> row_offsets;
-  std::vector<std::size_t> column_indices;
-};
-
 /// @brief Owns full/free/constrained numbering, scatter maps, and CSR pattern.
 class DofManager {
  public:

include/fesa/math/matrix.h

@@ -32,6 +32,26 @@ class Matrix {
   /// @brief Returns the column count.
   std::size_t Columns() const noexcept;
 
+  /// @brief Returns mutable row-major contiguous storage.
+  /// @note Borrows Rows()*Columns() entries until storage is moved, assigned
+  /// or destroyed.
+  double* Data() noexcept;
+
+  /// @brief Returns immutable row-major contiguous storage.
+  /// @note Borrows Rows()*Columns() entries until storage is moved, assigned
+  /// or destroyed.
+  const double* Data() const noexcept;
+
+  /// @brief Computes the robust Frobenius norm through the dense backend.
+  /// @note Empty storage has zero norm; nonfinite values propagate as in Vector.
+  /// @throws std::length_error if storage exceeds the backend integer range.
+  double Norm() const;
+
+  /// @brief Scales every entry by alpha through the dense backend.
+  /// @note Empty storage is unchanged; nonfinite values follow BLAS semantics.
+  /// @throws std::length_error if storage exceeds the backend integer range.
+  void Scale(double alpha);
+
   /// @brief Returns a bounds-checked mutable entry.
   /// @throws std::out_of_range if the index is outside the matrix.
   double& operator()(std::size_t row, std::size_t column);

include/fesa/math/sparse_matrix.h

@@ -5,12 +5,11 @@
 #include <vector>
 
 #include "fesa/core/status.h"
+#include "fesa/math/sparse_pattern.h"
 #include "fesa/math/vector.h"
 
 namespace fesa {
 
-struct SparsePattern;
-
 /// @brief Carries one deterministic element-local COO contribution.
 struct CooContribution {
   std::size_t row;

include/fesa/math/sparse_pattern.h

@@ -0,0 +1,18 @@
+#ifndef FESA_MATH_SPARSE_PATTERN_H_
+#define FESA_MATH_SPARSE_PATTERN_H_
+
+#include <cstddef>
+#include <vector>
+
+namespace fesa {
+
+/// @brief Stores the stable full-space CSR pattern.
+struct SparsePattern {
+  std::vector<std::size_t> row_offsets;
+  std::vector<std::size_t> column_indices;
+};
+
+
+}  // namespace fesa
+
+#endif  // FESA_MATH_SPARSE_PATTERN_H_

include/fesa/model/domain.h

@@ -11,6 +11,8 @@
 #include "fesa/constraints/boundary_condition.h"
 #include "fesa/constraints/prescribed_displacement.h"
 #include "fesa/core/status.h"
+#include "fesa/elements/ds4_thermal.h"
+#include "fesa/materials/isotropic_thermal_material.h"
 #include "fesa/loads/concentrated_nodal_load.h"
 #include "fesa/loads/load.h"
 #include "fesa/model/model_types.h"

include/fesa/model/model_types.h

@@ -13,12 +13,11 @@
 
 #include "fesa/core/diagnostic.h"
 #include "fesa/core/source_identity.h"
-#include "fesa/elements/ds4_thermal.h"
-#include "fesa/elements/euler_beam_3d.h"
+#include "fesa/elements/euler_beam_3d_definition.h"
 #include "fesa/elements/hex8_definition.h"
-#include "fesa/elements/mitc4_shell.h"
+#include "fesa/elements/mitc4_shell_definition.h"
+#include "fesa/elements/thermal_dof_component.h"
 #include "fesa/materials/isotropic_linear_elastic_material.h"
-#include "fesa/materials/isotropic_thermal_material.h"
 #include "fesa/properties/general_beam_section.h"
 #include "fesa/properties/shell_section.h"
 #include "fesa/properties/solid_section.h"
@@ -302,16 +301,6 @@ struct ThermalInitialConditionDefinition {
   SourceLocation location;
 };
 
-/// @brief Identifies the fixed bottom-to-top thermal station source DOFs.
-/// @note This is separate from the six-component structural DofComponent.
-enum class ThermalDofComponent : int {
-  kBottom = 11,
-  kLower = 12,
-  kMiddle = 13,
-  kUpper = 14,
-  kTop = 15
-};
-
 /// @brief Stores one prescribed thermal source DOF value.
 struct ThermalBoundaryConditionDefinition {
   EntityIndex node_index;

include/fesa/model/source_target_resolver.h

@@ -38,6 +38,14 @@ class SourceTargetIndex {
   /// @return An owning index that preserves Domain declaration order.
   static SourceTargetIndex FromDomain(const Domain& domain);
 
+  /// @brief Copies node and set identities before Domain ownership begins.
+  /// @param nodes Semantic nodes in stable expanded declaration order.
+  /// @param node_sets Node memberships in stable source order.
+  /// @return An owning node-only index preserving raw spelling and scope.
+  /// @note The returned index outlives its inputs; no Domain is constructed.
+  static SourceTargetIndex FromNodeDefinitions(
+      const std::vector<Node>& nodes, const std::vector<NodeSet>& node_sets);
+
   /// @brief Returns owned entries without exposing mutable index state.
   const std::vector<SourceTargetIndexEntry>& Entries() const noexcept;
 

include/fesa/results/prepared_results_writer.h

@@ -0,0 +1,39 @@
+#ifndef FESA_RESULTS_PREPARED_RESULTS_WRITER_H_
+#define FESA_RESULTS_PREPARED_RESULTS_WRITER_H_
+
+#include <filesystem>
+#include <vector>
+
+#include "fesa/analysis/prepared_analysis_outcome.h"
+#include "fesa/core/diagnostic.h"
+#include "fesa/core/status.h"
+
+namespace fesa {
+
+class Domain;
+class ResultsWriter;
+class NonlinearResultsWriter;
+class EigenResultsWriter;
+class DynamicResultsWriter;
+class ThermalResultsWriter;
+class SolidResultsWriter;
+
+/// @brief Routes one completed typed outcome to its authoritative writer.
+/// @pre Domain, outcome, diagnostics, and adapters remain alive for this call.
+/// The caller has closed its analysis log successfully before publication.
+/// @param results_path Explicit output path, retaining each writer's contract.
+/// @note Optional adapters are required only for their matching outcome family.
+/// @return The selected writer's Status after candidate validation/finalization,
+/// or the existing missing-adapter output failure without invoking a writer.
+Status WritePreparedAnalysisResult(
+    const std::filesystem::path& results_path, const Domain& domain,
+    const PreparedAnalysisOutcome& outcome,
+    const std::vector<Diagnostic>& diagnostics, ResultsWriter& linear_writer,
+    NonlinearResultsWriter& nonlinear_writer, EigenResultsWriter& eigen_writer,
+    DynamicResultsWriter* dynamic_writer = nullptr,
+    ThermalResultsWriter* thermal_writer = nullptr,
+    SolidResultsWriter* solid_writer = nullptr);
+
+}  // namespace fesa
+
+#endif  // FESA_RESULTS_PREPARED_RESULTS_WRITER_H_

include/fesa/solvers/eigen/eigen_solver.h

@@ -0,0 +1,99 @@
+#ifndef FESA_SOLVERS_EIGEN_EIGEN_SOLVER_H_
+#define FESA_SOLVERS_EIGEN_EIGEN_SOLVER_H_
+
+#include <cstddef>
+#include <cstdint>
+#include <string>
+#include <vector>
+
+#include "fesa/core/status.h"
+#include "fesa/math/matrix.h"
+
+namespace fesa {
+
+class SparseMatrix;
+
+/// @brief Records one deterministic private-backend invocation.
+struct FeastBackendCall {
+  std::size_t ordinal;
+  std::string kind;
+  std::string purpose;
+  double lower;
+  double upper;
+  std::size_t allocated_m0;
+  int info;
+  bool count_available;
+  std::size_t count;
+  bool loop_available;
+  int loop;
+  bool epsout_available;
+  double epsout;
+  std::string outcome;
+  std::string decision_reason;
+};
+
+/// @brief Owns the complete validated FEAST interval result before public N
+/// selection.
+struct FeastEigenResult {
+  std::size_t requested_modes;
+  std::vector<double> eigenvalues;
+  Matrix eigenvectors;
+  double operator_scale;
+  std::vector<std::size_t> column_ids;
+  std::vector<bool> backend_res_available;
+  std::vector<double> backend_res;
+  std::vector<double> normalized_eigenvalues;
+  std::vector<double> whitened_residuals;
+  double gram_error;
+  std::vector<FeastBackendCall> backend_calls;
+  std::vector<std::int64_t> base_fpm;
+  std::string runtime_version;
+  std::string integer_abi;
+  std::size_t thread_count;
+  std::uint64_t seed;
+  double enclosure_lower;
+  double enclosure_upper;
+  double solve_lower;
+  double solve_upper;
+  std::string upper_search_termination;
+};
+
+/// @brief Solves symmetric standard or definite generalized eigenproblems.
+/// @note Inputs remain caller-owned and are borrowed only for each call.
+class EigenSolver {
+ public:
+  /// @brief Destroys a backend-neutral eigen solver.
+  virtual ~EigenSolver() = default;
+
+  /// @brief Computes all validated interval pairs for a requested lowest-mode
+  /// prefix.
+  /// @param whitened_operator Symmetric physical-lambda operator after
+  /// whitening.
+  /// @param requested_modes Number of lowest modes eventually exposed by the
+  /// caller.
+  /// @param zero_operator_scale Positive physical scale used only when A is
+  /// exactly zero.
+  /// @return Sorted all-c eigenpairs in physical lambda units or a solver
+  /// failure.
+  virtual Result<FeastEigenResult> Solve(
+      const SparseMatrix& whitened_operator, std::size_t requested_modes,
+      double zero_operator_scale) const = 0;
+
+  /// @brief Solves the original sparse symmetric definite K/M pencil.
+  /// @param mass_lower_bound Certified positive lower spectral bound of M,
+  /// including floating-point assembly uncertainty; never a diagonal estimate.
+  /// @param classification_scale Positive max |Kii|/Mii in physical units.
+  /// @note Eigenvectors are mass-normalized. For this API the historical
+  /// whitened_residuals field contains original-pencil eta_r; no whitening
+  /// is performed. Intervals/eigenvalues in normalized backend evidence use
+  /// classification_scale, while eigenvalues are returned in physical units.
+  virtual Result<FeastEigenResult> SolveGeneralized(
+      const SparseMatrix& stiffness, const SparseMatrix& mass,
+      std::size_t requested_modes, double mass_lower_bound,
+      double classification_scale) const = 0;
+
+};
+
+}  // namespace fesa
+
+#endif  // FESA_SOLVERS_EIGEN_EIGEN_SOLVER_H_

include/fesa/solvers/eigen/mkl_feast_eigen_solver.h

@@ -1,65 +1,12 @@
 #ifndef FESA_SOLVERS_EIGEN_MKL_FEAST_EIGEN_SOLVER_H_
 #define FESA_SOLVERS_EIGEN_MKL_FEAST_EIGEN_SOLVER_H_
 
-#include <cstddef>
-#include <cstdint>
-#include <string>
-#include <vector>
-
-#include "fesa/core/status.h"
-#include "fesa/math/matrix.h"
+#include "fesa/solvers/eigen/eigen_solver.h"
 
 namespace fesa {
 
-class SparseMatrix;
-
-/// @brief Records one deterministic private-backend invocation.
-struct FeastBackendCall {
-  std::size_t ordinal;
-  std::string kind;
-  std::string purpose;
-  double lower;
-  double upper;
-  std::size_t allocated_m0;
-  int info;
-  bool count_available;
-  std::size_t count;
-  bool loop_available;
-  int loop;
-  bool epsout_available;
-  double epsout;
-  std::string outcome;
-  std::string decision_reason;
-};
-
-/// @brief Owns the complete validated FEAST interval result before public N
-/// selection.
-struct FeastEigenResult {
-  std::size_t requested_modes;
-  std::vector<double> eigenvalues;
-  Matrix eigenvectors;
-  double operator_scale;
-  std::vector<std::size_t> column_ids;
-  std::vector<bool> backend_res_available;
-  std::vector<double> backend_res;
-  std::vector<double> normalized_eigenvalues;
-  std::vector<double> whitened_residuals;
-  double gram_error;
-  std::vector<FeastBackendCall> backend_calls;
-  std::vector<std::int64_t> base_fpm;
-  std::string runtime_version;
-  std::string integer_abi;
-  std::size_t thread_count;
-  std::uint64_t seed;
-  double enclosure_lower;
-  double enclosure_upper;
-  double solve_lower;
-  double solve_upper;
-  std::string upper_search_termination;
-};
-
 /// @brief Adapts standard and symmetric-definite sparse pencils to FEAST.
-class MklFeastEigenSolver final {
+class MklFeastEigenSolver final : public EigenSolver {
  public:
   /// @brief Computes all validated interval pairs for a requested lowest-mode
   /// prefix.
@@ -74,8 +21,8 @@ class MklFeastEigenSolver final {
   /// @note The implementation fixes oneMKL local thread count to one during
   /// every call.
   Result<FeastEigenResult> Solve(const SparseMatrix& whitened_operator,
-                                 std::size_t requested_modes,
-                                 double zero_operator_scale) const;
+                                std::size_t requested_modes,
+                                double zero_operator_scale) const override;
   /// @brief Solves the original sparse symmetric definite K/M pencil.
   /// @param mass_lower_bound Certified positive lower spectral bound of M,
   /// including floating-point assembly uncertainty; never a diagonal estimate.
@@ -86,16 +33,16 @@ class MklFeastEigenSolver final {
   /// classification_scale, while eigenvalues are returned in physical units.
   Result<FeastEigenResult> SolveGeneralized(const SparseMatrix& stiffness,
                                             const SparseMatrix& mass,
-                                            std::size_t requested_modes,
+                                           std::size_t requested_modes,
                                             double mass_lower_bound,
-                                            double classification_scale) const;
+                                            double classification_scale) const override;
 
  private:
   /// @brief Shares deterministic count/search controls without changing
   /// pencils.
   Result<FeastEigenResult> SolveImpl(const SparseMatrix& stiffness,
                                      const SparseMatrix* mass,
-                                     std::size_t requested_modes,
+                                    std::size_t requested_modes,
                                      double physical_scale,
                                      double mass_lower_bound) const;
 };

msvc/AGENTS.md

@@ -0,0 +1,17 @@
+# 직접 유지하는 MSVC 빌드
+
+이 영역은 FESA 솔루션의 solver library·CLI·별도 테스트 프로젝트와 공통 옵션·DLL 준비를
+소유한다. CMake가 생성한 프로젝트로 교체하거나 빌드 전에 CMake를 숨겨서 호출하지 않는다.
+요소 수식·검사 본문·기준 데이터는 이 영역의 소유가 아니다.
+
+- Source 추가·이동·제거는 대응하는 CMake target 목록과 같은 변경 단위로 처리한다.
+  한 owner가 두 목록을 대조하며 solver와 검사 본문을 빌드 경로별로 복제하지 않는다.
+- `Fesa.Common.props`와 `Fesa.Runtime.targets`의 CRT·산술·define·link·runtime staging을
+  함께 확인한다. 개인 설치 경로는 환경변수 또는 ignored `Fesa.Local.props`로 주입한다.
+- AVX2 옵션은 전용 Hex8 source에만 둔다. Dispatch source와 나머지 target으로 확장하지 않는다.
+  외부 GoogleTest source에 FESA 제품의 `/W4 /WX` 정책을 강제하지 않는다.
+- `MSBuild FESA.sln /m:2 /p:Configuration=Debug /p:Platform=x64`는 저장소 root의
+  VS x64 개발 환경에서 실행한다. 별도 테스트 executable이 같은 solver library를 연결하고
+  실행 파일 곁의 configuration별 DLL도 준비됐는지 확인한다. 빌드 성공은 검사 통과가 아니다.
+- 빌드 설정을 바꾸면 CMake와 실제 source·옵션·link·DLL 및 발견한 검사 identity를 대조한다.
+  기존 실행 로그와 바이너리를 덮어쓰지 말고 변경 전후 근거를 구분한다.

msvc/Fesa.Common.props

@@ -0,0 +1,75 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <!-- Override installation roots with environment variables or this ignored sheet. -->
+  <Import Project="Fesa.Local.props" Condition="Exists('Fesa.Local.props')" />
+  <PropertyGroup>
+    <FesaRoot>$([System.IO.Path]::GetFullPath('$(MSBuildThisFileDirectory)..\'))</FesaRoot>
+    <FesaBuildRoot>$(FesaRoot).build\native\$(Configuration)\</FesaBuildRoot>
+    <FesaRootForward>$(FesaRoot.Replace('\','/').TrimEnd('/'))</FesaRootForward>
+    <FesaBuildRootForward>$(FesaBuildRoot.Replace('\','/').TrimEnd('/'))</FesaBuildRootForward>
+    <OutDir>$(FesaBuildRoot)tests\</OutDir>
+    <OutDir Condition="'$(MSBuildProjectName)'=='fesa_cli'">$(FesaBuildRoot)src\fesa\</OutDir>
+    <OutDir Condition="'$(ConfigurationType)'=='StaticLibrary'">$(FesaBuildRoot)lib\</OutDir>
+    <IntDir>$(FesaBuildRoot)obj\$(MSBuildProjectName)\</IntDir>
+    <TargetName Condition="'$(MSBuildProjectName)'=='fesa_cli'">fesa</TargetName>
+    <TbbSuffix Condition="'$(Configuration)'=='Debug'">_debug</TbbSuffix>
+  </PropertyGroup>
+  <PropertyGroup>
+    <FesaExternalOptions Condition="'$(MSBuildProjectName)'=='fesa_solver'">/external:I&quot;$(FESA_MKL_ROOT)\include&quot; /external:I&quot;$(FESA_TBB_ROOT)\include&quot; /external:I&quot;$(FESA_HDF5_ROOT)\include&quot; /external:W0</FesaExternalOptions>
+    <FesaExternalOptions Condition="'$(MSBuildProjectName)'=='fesa_unit_tests' Or '$(MSBuildProjectName)'=='fesa_integration_tests' Or '$(MSBuildProjectName)'=='fesa_reference_tests'">/external:I&quot;$(FESA_HDF5_ROOT)\include&quot; /external:I&quot;$(FESA_GTEST_SOURCE_DIR)\googletest\include&quot; /external:I&quot;$(FESA_GTEST_SOURCE_DIR)\googletest&quot; /external:W0</FesaExternalOptions>
+    <FesaExternalOptions Condition="'$(MSBuildProjectName)'=='fesa_unit_tests'">$(FesaExternalOptions) /external:I&quot;$(FESA_MKL_ROOT)\include&quot;</FesaExternalOptions>
+  </PropertyGroup>
+  <ItemDefinitionGroup>
+    <ClCompile>
+      <LanguageStandard>stdcpp17</LanguageStandard>
+      <SupportJustMyCode>false</SupportJustMyCode>
+      <ExceptionHandling>Sync</ExceptionHandling>
+      <WarningLevel>Level3</WarningLevel>
+      <TreatWarningAsError>false</TreatWarningAsError>
+      <WarningLevel Condition="'$(MSBuildProjectName)'=='fesa_solver' Or '$(MSBuildProjectName)'=='fesa_cli'">Level4</WarningLevel>
+      <TreatWarningAsError Condition="'$(MSBuildProjectName)'=='fesa_solver' Or '$(MSBuildProjectName)'=='fesa_cli'">true</TreatWarningAsError>
+      <RuntimeLibrary Condition="'$(Configuration)'=='Debug'">MultiThreadedDebugDLL</RuntimeLibrary>
+      <RuntimeLibrary Condition="'$(Configuration)'=='Release'">MultiThreadedDLL</RuntimeLibrary>
+      <Optimization Condition="'$(Configuration)'=='Debug'">Disabled</Optimization>
+      <InlineFunctionExpansion Condition="'$(Configuration)'=='Debug'">Disabled</InlineFunctionExpansion>
+      <BasicRuntimeChecks Condition="'$(Configuration)'=='Debug'">EnableFastChecks</BasicRuntimeChecks>
+      <Optimization Condition="'$(Configuration)'=='Release'">MaxSpeed</Optimization>
+      <InlineFunctionExpansion Condition="'$(Configuration)'=='Release'">AnySuitable</InlineFunctionExpansion>
+      <DebugInformationFormat Condition="'$(Configuration)'=='Debug'">ProgramDatabase</DebugInformationFormat>
+      <DebugInformationFormat Condition="'$(Configuration)'=='Release' And ('$(MSBuildProjectName)'=='fesa_solver' Or '$(MSBuildProjectName)'=='fesa_cli')">ProgramDatabase</DebugInformationFormat>
+      <FloatingPointModel>Precise</FloatingPointModel>
+      <PreprocessorDefinitions>WIN32;_WINDOWS;%(PreprocessorDefinitions)</PreprocessorDefinitions>
+      <PreprocessorDefinitions Condition="'$(Configuration)'=='Release'">NDEBUG;WIN32;_WINDOWS;%(PreprocessorDefinitions)</PreprocessorDefinitions>
+      <AdditionalIncludeDirectories>$(FesaRoot)include;%(AdditionalIncludeDirectories)</AdditionalIncludeDirectories>
+      <AdditionalIncludeDirectories Condition="'$(MSBuildProjectName)'=='fesa_solver' Or '$(MSBuildProjectName)'=='fesa_unit_tests' Or '$(MSBuildProjectName)'=='fesa_integration_tests'">$(FesaRoot)include;$(FesaRoot)src\fesa;%(AdditionalIncludeDirectories)</AdditionalIncludeDirectories>
+      <AdditionalOptions>$(FesaExternalOptions) /MP2 %(AdditionalOptions)</AdditionalOptions>
+      <ExternalWarningLevel>TurnOffAllWarnings</ExternalWarningLevel>
+    </ClCompile>
+    <Link>
+      <TargetMachine>MachineX64</TargetMachine>
+      <SubSystem>Console</SubSystem>
+      <GenerateDebugInformation Condition="'$(Configuration)'=='Release' And '$(MSBuildProjectName)'=='fesa_cli'">true</GenerateDebugInformation>
+      <OptimizeReferences Condition="'$(Configuration)'=='Release' And '$(MSBuildProjectName)'=='fesa_cli'">true</OptimizeReferences>
+      <EnableCOMDATFolding Condition="'$(Configuration)'=='Release' And '$(MSBuildProjectName)'=='fesa_cli'">true</EnableCOMDATFolding>
+      <GenerateDebugInformation Condition="'$(Configuration)'=='Debug'">true</GenerateDebugInformation>
+      <AdditionalLibraryDirectories>$(FESA_MKL_ROOT)\lib;$(FESA_OMP_ROOT)\lib;$(FESA_TBB_ROOT)\lib;$(FESA_HDF5_ROOT)\lib;%(AdditionalLibraryDirectories)</AdditionalLibraryDirectories>
+      <AdditionalDependencies>mkl_intel_ilp64_dll.lib;mkl_intel_thread_dll.lib;mkl_core_dll.lib;libiomp5md.lib;tbb12$(TbbSuffix).lib;hdf5.lib;shlwapi.lib;%(AdditionalDependencies)</AdditionalDependencies>
+    </Link>
+  </ItemDefinitionGroup>
+  <ItemDefinitionGroup Condition="'$(MSBuildProjectName)'=='fesa_solver'">
+    <ClCompile><PreprocessorDefinitions>MKL_ILP64;H5_BUILT_AS_DYNAMIC_LIB;__TBB_NO_IMPLICIT_LINKAGE=1;%(PreprocessorDefinitions)</PreprocessorDefinitions></ClCompile>
+  </ItemDefinitionGroup>
+  <ItemDefinitionGroup Condition="'$(MSBuildProjectName)'=='fesa_unit_tests'">
+    <ClCompile><PreprocessorDefinitions>MKL_ILP64;%(PreprocessorDefinitions)</PreprocessorDefinitions></ClCompile>
+  </ItemDefinitionGroup>
+  <ItemDefinitionGroup Condition="'$(MSBuildProjectName)'=='fesa_unit_tests' Or '$(MSBuildProjectName)'=='fesa_integration_tests' Or '$(MSBuildProjectName)'=='fesa_reference_tests'">
+    <ClCompile><PreprocessorDefinitions>H5_BUILT_AS_DYNAMIC_LIB;%(PreprocessorDefinitions)</PreprocessorDefinitions></ClCompile>
+  </ItemDefinitionGroup>
+  <ItemDefinitionGroup Condition="'$(MSBuildProjectName)'=='gtest'">
+    <ClCompile>
+      <AdditionalIncludeDirectories>$(FESA_GTEST_SOURCE_DIR)\googletest\include;$(FESA_GTEST_SOURCE_DIR)\googletest</AdditionalIncludeDirectories>
+      <AdditionalOptions>/utf-8 /J %(AdditionalOptions)</AdditionalOptions>
+      <PreprocessorDefinitions>GTEST_HAS_PTHREAD=0;_HAS_EXCEPTIONS=1;%(PreprocessorDefinitions)</PreprocessorDefinitions>
+    </ClCompile>
+  </ItemDefinitionGroup>
+</Project>

msvc/Fesa.Runtime.targets

@@ -0,0 +1,23 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <Target Name="ValidateFesaDependencies" BeforeTargets="PrepareForBuild">
+    <Error Condition="'$(Platform)'!='x64'" Text="FESA requires MSVC x64." />
+    <Error Condition="!Exists('$(FESA_GTEST_SOURCE_DIR)\googletest\src\gtest-all.cc')" Text="Set FESA_GTEST_SOURCE_DIR to the approved local GoogleTest source checkout." />
+    <Error Condition="!Exists('$(FESA_MKL_ROOT)\lib\mkl_intel_ilp64_dll.lib')" Text="Set FESA_MKL_ROOT to the oneMKL installation root." />
+    <Error Condition="!Exists('$(FESA_TBB_ROOT)\lib\tbb12$(TbbSuffix).lib')" Text="Set FESA_TBB_ROOT to the oneTBB installation root." />
+    <Error Condition="!Exists('$(FESA_HDF5_ROOT)\lib\hdf5.lib')" Text="Set FESA_HDF5_ROOT to the shared HDF5 installation root." />
+    <Error Condition="!Exists('$(FESA_OMP_ROOT)\bin\libiomp5md.dll') Or !Exists('$(FESA_OMP_ROOT)\bin\libmmd.dll')" Text="Set FESA_OMP_ROOT to the Intel compiler runtime installation root." />
+  </Target>
+  <Target Name="StageFesaRuntime" AfterTargets="Build" Condition="'$(ConfigurationType)'=='Application'">
+    <ItemGroup>
+      <FesaMklThread Include="$(FESA_MKL_ROOT)\bin\mkl_intel_thread.*.dll" />
+      <FesaMklCore Include="$(FESA_MKL_ROOT)\bin\mkl_core.*.dll" />
+      <FesaMklDispatch Include="$(FESA_MKL_ROOT)\bin\mkl_def.*.dll" />
+      <FesaRuntime Include="@(FesaMklThread);@(FesaMklCore);@(FesaMklDispatch);$(FESA_TBB_ROOT)\bin\tbb12$(TbbSuffix).dll;$(FESA_OMP_ROOT)\bin\libiomp5md.dll;$(FESA_OMP_ROOT)\bin\libmmd.dll;$(FESA_HDF5_ROOT)\bin\hdf5.dll" />
+    </ItemGroup>
+    <Error Condition="'@(FesaMklThread)'==''" Text="The oneMKL Intel-thread runtime DLL was not resolved." />
+    <Error Condition="'@(FesaMklCore)'==''" Text="The oneMKL core runtime DLL was not resolved." />
+    <Error Condition="'@(FesaMklDispatch)'==''" Text="The oneMKL default-dispatch runtime DLL was not resolved." />
+    <Copy SourceFiles="@(FesaRuntime)" DestinationFolder="$(OutDir)" SkipUnchangedFiles="true" />
+  </Target>
+</Project>

msvc/fesa_cli.vcxproj

@@ -0,0 +1,18 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup Label="ProjectConfigurations"><ProjectConfiguration Include="Debug|x64"><Configuration>Debug</Configuration><Platform>x64</Platform></ProjectConfiguration><ProjectConfiguration Include="Release|x64"><Configuration>Release</Configuration><Platform>x64</Platform></ProjectConfiguration></ItemGroup>
+  <PropertyGroup Label="Globals"><ProjectGuid>{6DE2CFFA-D9B3-5E14-BEBD-5DFAB2B5290B}</ProjectGuid><Keyword>Win32Proj</Keyword><WindowsTargetPlatformVersion>10.0</WindowsTargetPlatformVersion></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
+  <PropertyGroup Label="Configuration"><ConfigurationType>Application</ConfigurationType><PlatformToolset>v145</PlatformToolset><UseDebugLibraries Condition="'$(Configuration)'=='Debug'">true</UseDebugLibraries></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
+  <Import Project="Fesa.Common.props" />
+
+  <ItemGroup>
+    <ClCompile Include="..\src\fesa\app\main.cpp" />
+  </ItemGroup>
+  <ItemGroup>
+    <ProjectReference Include="fesa_solver.vcxproj"><Project>{3AEC39D9-4641-5161-9107-265EB50CA882}</Project><LinkLibraryDependencies>true</LinkLibraryDependencies></ProjectReference>
+  </ItemGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
+  <Import Project="Fesa.Runtime.targets" />
+</Project>

msvc/fesa_integration_tests.vcxproj

@@ -0,0 +1,30 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup Label="ProjectConfigurations"><ProjectConfiguration Include="Debug|x64"><Configuration>Debug</Configuration><Platform>x64</Platform></ProjectConfiguration><ProjectConfiguration Include="Release|x64"><Configuration>Release</Configuration><Platform>x64</Platform></ProjectConfiguration></ItemGroup>
+  <PropertyGroup Label="Globals"><ProjectGuid>{7770C26B-DBFE-505D-8788-8B7EFD9A5A70}</ProjectGuid><Keyword>Win32Proj</Keyword><WindowsTargetPlatformVersion>10.0</WindowsTargetPlatformVersion></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
+  <PropertyGroup Label="Configuration"><ConfigurationType>Application</ConfigurationType><PlatformToolset>v145</PlatformToolset><UseDebugLibraries Condition="'$(Configuration)'=='Debug'">true</UseDebugLibraries></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
+  <Import Project="Fesa.Common.props" />
+
+  <ItemGroup>
+    <ClCompile Include="..\tests\integration\analysis\linear_static_analysis_test.cpp" />
+    <ClCompile Include="..\tests\integration\analysis\linear_frequency_procedure_test.cpp" />
+    <ClCompile Include="..\tests\integration\analysis\shell_surface_pressure_linear_test.cpp" />
+    <ClCompile Include="..\tests\integration\analysis\shell_surface_pressure_nonlinear_test.cpp" />
+    <ClCompile Include="..\tests\integration\analysis\nonlinear_static_procedure_test.cpp" />
+    <ClCompile Include="..\tests\integration\analysis\thermal_physics_test.cpp" />
+    <ClCompile Include="..\tests\integration\app\fesa_application_test.cpp" />
+    <ClCompile Include="..\tests\integration\app\eigen_application_test.cpp" />
+    <ClCompile Include="..\tests\integration\app\shell_surface_pressure_application_test.cpp" />
+    <ClCompile Include="..\tests\integration\app\thermal_application_test.cpp" />
+    <ClCompile Include="..\tests\integration\app\solid_application_test.cpp" />
+  </ItemGroup>
+  <ItemGroup>
+    <ProjectReference Include="fesa_solver.vcxproj"><Project>{3AEC39D9-4641-5161-9107-265EB50CA882}</Project><LinkLibraryDependencies>true</LinkLibraryDependencies></ProjectReference>
+    <ProjectReference Include="gtest.vcxproj"><Project>{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}</Project><LinkLibraryDependencies>true</LinkLibraryDependencies></ProjectReference>
+    <ProjectReference Include="fesa_cli.vcxproj"><Project>{6DE2CFFA-D9B3-5E14-BEBD-5DFAB2B5290B}</Project><LinkLibraryDependencies>false</LinkLibraryDependencies></ProjectReference>
+  </ItemGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
+  <Import Project="Fesa.Runtime.targets" />
+</Project>

msvc/fesa_reference_tests.vcxproj

@@ -0,0 +1,35 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup Label="ProjectConfigurations"><ProjectConfiguration Include="Debug|x64"><Configuration>Debug</Configuration><Platform>x64</Platform></ProjectConfiguration><ProjectConfiguration Include="Release|x64"><Configuration>Release</Configuration><Platform>x64</Platform></ProjectConfiguration></ItemGroup>
+  <PropertyGroup Label="Globals"><ProjectGuid>{330D2DFB-E57D-517D-A795-F1EA620B69F0}</ProjectGuid><Keyword>Win32Proj</Keyword><WindowsTargetPlatformVersion>10.0</WindowsTargetPlatformVersion></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
+  <PropertyGroup Label="Configuration"><ConfigurationType>Application</ConfigurationType><PlatformToolset>v145</PlatformToolset><UseDebugLibraries Condition="'$(Configuration)'=='Debug'">true</UseDebugLibraries></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
+  <Import Project="Fesa.Common.props" />
+  <ItemDefinitionGroup><ClCompile><PreprocessorDefinitions>FESA_TEST_SOURCE_DIR="$(FesaRootForward)";FESA_TEST_BINARY_DIR="$(FesaBuildRootForward)";%(PreprocessorDefinitions)</PreprocessorDefinitions></ClCompile></ItemDefinitionGroup>
+  <ItemGroup>
+    <ClCompile Include="..\tests\reference\reference_tolerance_policy.cpp" />
+    <ClCompile Include="..\tests\reference\eigen_reference_comparison.cpp" />
+    <ClCompile Include="..\tests\reference\eigen_reference_comparison_test.cpp" />
+    <ClCompile Include="..\tests\reference\eigen_reference_cases_test.cpp" />
+    <ClCompile Include="..\tests\reference\reference_tolerance_policy_test.cpp" />
+    <ClCompile Include="..\tests\reference\reference_comparison.cpp" />
+    <ClCompile Include="..\tests\reference\reference_comparison_test.cpp" />
+    <ClCompile Include="..\tests\reference\b33_reference_comparison_test.cpp" />
+    <ClCompile Include="..\tests\reference\mitc4_reference_comparison.cpp" />
+    <ClCompile Include="..\tests\reference\mitc4_reference_comparison_test.cpp" />
+    <ClCompile Include="..\tests\reference\mitc4_reference_cases_test.cpp" />
+    <ClCompile Include="..\tests\reference\nonlinear_static_reference_comparison.cpp" />
+    <ClCompile Include="..\tests\reference\nonlinear_static_reference_cases_test.cpp" />
+    <ClCompile Include="..\tests\reference\shell_surface_pressure_reference_test.cpp" />
+    <ClCompile Include="..\tests\reference\thermal_reference_comparison.cpp" />
+    <ClCompile Include="..\tests\reference\thermal_reference_comparison_test.cpp" />
+    <ClCompile Include="..\tests\reference\thermal_reference_cases_test.cpp" />
+  </ItemGroup>
+  <ItemGroup>
+    <ProjectReference Include="fesa_solver.vcxproj"><Project>{3AEC39D9-4641-5161-9107-265EB50CA882}</Project><LinkLibraryDependencies>true</LinkLibraryDependencies></ProjectReference>
+    <ProjectReference Include="gtest.vcxproj"><Project>{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}</Project><LinkLibraryDependencies>true</LinkLibraryDependencies></ProjectReference>
+  </ItemGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
+  <Import Project="Fesa.Runtime.targets" />
+</Project>

msvc/fesa_solver.vcxproj

@@ -0,0 +1,118 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup Label="ProjectConfigurations"><ProjectConfiguration Include="Debug|x64"><Configuration>Debug</Configuration><Platform>x64</Platform></ProjectConfiguration><ProjectConfiguration Include="Release|x64"><Configuration>Release</Configuration><Platform>x64</Platform></ProjectConfiguration></ItemGroup>
+  <PropertyGroup Label="Globals"><ProjectGuid>{3AEC39D9-4641-5161-9107-265EB50CA882}</ProjectGuid><Keyword>Win32Proj</Keyword><WindowsTargetPlatformVersion>10.0</WindowsTargetPlatformVersion></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
+  <PropertyGroup Label="Configuration"><ConfigurationType>StaticLibrary</ConfigurationType><PlatformToolset>v145</PlatformToolset><UseDebugLibraries Condition="'$(Configuration)'=='Debug'">true</UseDebugLibraries></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
+  <Import Project="Fesa.Common.props" />
+  <ItemDefinitionGroup><ClCompile><PreprocessorDefinitions>FESA_HEX8_PAIR_AVX2=1;%(PreprocessorDefinitions)</PreprocessorDefinitions></ClCompile></ItemDefinitionGroup>
+  <ItemGroup>
+    <ClCompile Include="..\src\fesa\analysis\analysis_model.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\analysis_state.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\dynamic_analysis_state.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\eigen_reduction.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\hht_time_integration.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\hht_dynamic_algebra.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\hht_dynamic_assembly.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\hht_reduced_operators.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\hht_reduced_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\hht_dynamic_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\linear_frequency_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\linear_static_analysis.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\linear_static_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\newton_iteration_log.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\nonlinear_analysis_state.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\nonlinear_static_control.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\nonlinear_static_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\prepared_analysis.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\solid_dynamic_analysis_state.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\solid_frequency_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\solid_hht_dynamic_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\solid_static_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\solid_static_state.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\thermal_analysis_state.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\thermal_time_grid.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\thermal_transient_algebra.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\transient_heat_procedure.cpp" />
+    <ClCompile Include="..\src\fesa\app\fesa_application.cpp" />
+    <ClCompile Include="..\src\fesa\app\output_paths.cpp" />
+    <ClCompile Include="..\src\fesa\assembly\load_assembler.cpp" />
+    <ClCompile Include="..\src\fesa\assembly\parallel_for.cpp" />
+    <ClCompile Include="..\src\fesa\assembly\sparse_assembler.cpp" />
+    <ClCompile Include="..\src\fesa\assembly\surface_pressure_assembler.cpp" />
+    <ClCompile Include="..\src\fesa\assembly\thermal_assembler.cpp" />
+    <ClCompile Include="..\src\fesa\build_info.cpp" />
+    <ClCompile Include="..\src\fesa\constraints\essential_constraint_policy.cpp" />
+    <ClCompile Include="..\src\fesa\constraints\prescribed_displacement.cpp" />
+    <ClCompile Include="..\src\fesa\core\ascii.cpp" />
+    <ClCompile Include="..\src\fesa\core\diagnostic.cpp" />
+    <ClCompile Include="..\src\fesa\core\status.cpp" />
+    <ClCompile Include="..\src\fesa\elements\element_capabilities.cpp" />
+    <ClCompile Include="..\src\fesa\elements\element_factory.cpp" />
+    <ClCompile Include="..\src\fesa\elements\hex8_element.cpp" />
+    <ClCompile Include="..\src\fesa\elements\hex8_high_low.cpp" />
+    <ClCompile Include="..\src\fesa\elements\hex8_pair_simd_dispatch.cpp" />
+    <ClCompile Include="..\src\fesa\elements\hex8_pair_simd_avx2.cpp"><EnableEnhancedInstructionSet>AdvancedVectorExtensions2</EnableEnhancedInstructionSet></ClCompile>
+    <ClCompile Include="..\src\fesa\elements\hex8_geometry.cpp" />
+    <ClCompile Include="..\src\fesa\elements\euler_beam_3d.cpp" />
+    <ClCompile Include="..\src\fesa\elements\finite_rotation.cpp" />
+    <ClCompile Include="..\src\fesa\elements\mitc4_shell.cpp" />
+    <ClCompile Include="..\src\fesa\elements\nonlinear_mitc4_shell.cpp" />
+    <ClCompile Include="..\src\fesa\elements\nonlinear_mitc4_inertia.cpp" />
+    <ClCompile Include="..\src\fesa\elements\thermal_shell.cpp" />
+    <ClCompile Include="..\src\fesa\elements\thermal_shell_geometry.cpp" />
+    <ClCompile Include="..\src\fesa\fem\dof_manager.cpp" />
+    <ClCompile Include="..\src\fesa\io\abaqus\domain_builder.cpp" />
+    <ClCompile Include="..\src\fesa\io\abaqus\domain_mapping_context.cpp" />
+    <ClCompile Include="..\src\fesa\io\abaqus\domain_mapper.cpp" />
+    <ClCompile Include="..\src\fesa\io\abaqus\input_reader.cpp" />
+    <ClCompile Include="..\src\fesa\io\abaqus\material_property_mapper.cpp" />
+    <ClCompile Include="..\src\fesa\io\abaqus\step_definition_mapper.cpp" />
+    <ClCompile Include="..\src\fesa\io\abaqus\surface_definition_mapper.cpp" />
+    <ClCompile Include="..\src\fesa\io\abaqus\topology_mapper.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\hdf5_atomic_file.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\dynamic_hdf5_results_writer.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\hdf5_model_writer.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\nonlinear_hdf5_results_writer.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\hdf5_primitives.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\hdf5_result_writer.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\hdf5_results_writer.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\eigen_hdf5_results_writer.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\eigen_hdf5_self_check.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\hdf5_self_check.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\thermal_hdf5_results_writer.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\thermal_hdf5_self_check.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\solid_hdf5_results_writer.cpp" />
+    <ClCompile Include="..\src\fesa\io\hdf5\solid_hdf5_self_check.cpp" />
+    <ClCompile Include="..\src\fesa\loads\concentrated_nodal_load.cpp" />
+    <ClCompile Include="..\src\fesa\loads\shell_surface_pressure.cpp" />
+    <ClCompile Include="..\src\fesa\materials\isotropic_linear_elastic_material.cpp" />
+    <ClCompile Include="..\src\fesa\materials\isotropic_thermal_material.cpp" />
+    <ClCompile Include="..\src\fesa\math\dense_blas_internal.cpp" />
+    <ClCompile Include="..\src\fesa\math\matrix.cpp" />
+    <ClCompile Include="..\src\fesa\math\sparse_matrix.cpp" />
+    <ClCompile Include="..\src\fesa\math\vector.cpp" />
+    <ClCompile Include="..\src\fesa\model\domain.cpp" />
+    <ClCompile Include="..\src\fesa\model\shell_geometry.cpp" />
+    <ClCompile Include="..\src\fesa\model\source_target_resolver.cpp" />
+    <ClCompile Include="..\src\fesa\properties\general_beam_section.cpp" />
+    <ClCompile Include="..\src\fesa\properties\shell_section.cpp" />
+    <ClCompile Include="..\src\fesa\results\analysis_state_commit.cpp" />
+    <ClCompile Include="..\src\fesa\results\beam_result_recovery.cpp" />
+    <ClCompile Include="..\src\fesa\results\global_equilibrium_recovery.cpp" />
+    <ClCompile Include="..\src\fesa\results\prepared_results_writer.cpp" />
+    <ClCompile Include="..\src\fesa\results\recovery_candidate.cpp" />
+    <ClCompile Include="..\src\fesa\results\result_recovery.cpp" />
+    <ClCompile Include="..\src\fesa\results\shell_result_recovery.cpp" />
+    <ClCompile Include="..\src\fesa\solvers\eigen\mkl_feast_eigen_solver.cpp" />
+    <ClCompile Include="..\src\fesa\solvers\linear\mkl_pardiso_solver.cpp" />
+    <ClCompile Include="..\src\fesa\solvers\linear\mkl_pardiso_tangent_solver.cpp" />
+    <ClCompile Include="..\src\fesa\solvers\linear\pardiso_session.cpp" />
+  </ItemGroup>
+  <ItemGroup>
+
+  </ItemGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
+  <Import Project="Fesa.Runtime.targets" />
+</Project>

msvc/fesa_unit_tests.vcxproj

@@ -0,0 +1,108 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup Label="ProjectConfigurations"><ProjectConfiguration Include="Debug|x64"><Configuration>Debug</Configuration><Platform>x64</Platform></ProjectConfiguration><ProjectConfiguration Include="Release|x64"><Configuration>Release</Configuration><Platform>x64</Platform></ProjectConfiguration></ItemGroup>
+  <PropertyGroup Label="Globals"><ProjectGuid>{42558F77-73F2-5CA7-8E3C-BB0E1646CD45}</ProjectGuid><Keyword>Win32Proj</Keyword><WindowsTargetPlatformVersion>10.0</WindowsTargetPlatformVersion></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
+  <PropertyGroup Label="Configuration"><ConfigurationType>Application</ConfigurationType><PlatformToolset>v145</PlatformToolset><UseDebugLibraries Condition="'$(Configuration)'=='Debug'">true</UseDebugLibraries></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
+  <Import Project="Fesa.Common.props" />
+
+  <ItemGroup>
+    <ClCompile Include="..\tests\unit\build_info_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\analysis_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\analysis_model_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\analysis_state_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\dynamic_analysis_state_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\eigen_reduction_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\eigen_mass_assembly_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\hht_time_integration_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\hht_shell_physics_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\hht_energy_verification_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\hht_temporal_verification_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\hht_dynamic_algebra_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\hht_reduced_shell_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\hht_dynamic_procedure_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\nonlinear_analysis_state_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\nonlinear_static_control_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\newton_iteration_log_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\solid_frequency_procedure_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\solid_hht_dynamic_procedure_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\solid_hht_temporal_verification_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\solid_static_procedure_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\solid_static_state_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\thermal_time_grid_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\thermal_analysis_state_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\transient_heat_procedure_test.cpp" />
+    <ClCompile Include="..\tests\unit\assembly\parallel_for_test.cpp" />
+    <ClCompile Include="..\tests\unit\assembly\load_assembler_test.cpp" />
+    <ClCompile Include="..\tests\unit\assembly\surface_pressure_assembler_test.cpp" />
+    <ClCompile Include="..\tests\unit\assembly\sparse_assembler_test.cpp" />
+    <ClCompile Include="..\tests\unit\assembly\thermal_assembler_test.cpp" />
+    <ClCompile Include="..\tests\unit\app\output_paths_test.cpp" />
+    <ClCompile Include="..\tests\unit\constraints\boundary_condition_test.cpp" />
+    <ClCompile Include="..\tests\unit\constraints\essential_constraints_test.cpp" />
+    <ClCompile Include="..\tests\unit\core\ascii_test.cpp" />
+    <ClCompile Include="..\tests\unit\core\diagnostic_test.cpp" />
+    <ClCompile Include="..\tests\unit\core\source_identity_test.cpp" />
+    <ClCompile Include="..\tests\unit\core\status_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\element_capabilities_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\element_factory_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\hex8_element_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\hex8_high_low_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\euler_beam_3d_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\finite_rotation_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\mitc4_shell_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\mitc4_shell_mass_contract_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\nonlinear_mitc4_shell_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\nonlinear_mitc4_inertia_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\nonlinear_mitc4_shell_tangent_test.cpp" />
+    <ClCompile Include="..\tests\unit\elements\thermal_shell_test.cpp" />
+    <ClCompile Include="..\tests\unit\fem\dof_manager_test.cpp" />
+    <ClCompile Include="..\tests\unit\math\dense_blas_internal_test.cpp" />
+    <ClCompile Include="..\tests\unit\math\high_low_arithmetic_test.cpp" />
+    <ClCompile Include="..\tests\unit\math\matrix_test.cpp" />
+    <ClCompile Include="..\tests\unit\math\sparse_matrix_test.cpp" />
+    <ClCompile Include="..\tests\unit\math\vector3_test.cpp" />
+    <ClCompile Include="..\tests\unit\math\vector_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\domain_mapping_components_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\domain_mapper_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\hex8_semantics_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\eigen_domain_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\hht_dynamic_domain_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\thermal_domain_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\input_reader_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\input_syntax_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\abaqus\shell_surface_pressure_domain_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\hdf5\hdf5_results_writer_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\hdf5\dynamic_hdf5_results_writer_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\hdf5\eigen_hdf5_results_writer_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\hdf5\nonlinear_hdf5_results_writer_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\hdf5\hdf5_writer_components_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\hdf5\thermal_hdf5_results_writer_test.cpp" />
+    <ClCompile Include="..\tests\unit\io\hdf5\solid_hdf5_results_writer_test.cpp" />
+    <ClCompile Include="..\tests\unit\loads\load_test.cpp" />
+    <ClCompile Include="..\tests\unit\loads\shell_surface_pressure_test.cpp" />
+    <ClCompile Include="..\tests\unit\model\domain_test.cpp" />
+    <ClCompile Include="..\tests\unit\model\thermal_semantics_test.cpp" />
+    <ClCompile Include="..\tests\unit\model\thermal_shell_geometry_test.cpp" />
+    <ClCompile Include="..\tests\unit\model\model_types_test.cpp" />
+    <ClCompile Include="..\tests\unit\model\shell_geometry_test.cpp" />
+    <ClCompile Include="..\tests\unit\model\source_target_resolver_test.cpp" />
+    <ClCompile Include="..\tests\unit\materials\material_test.cpp" />
+    <ClCompile Include="..\tests\unit\properties\element_property_test.cpp" />
+    <ClCompile Include="..\tests\unit\results\result_records_test.cpp" />
+    <ClCompile Include="..\tests\unit\results\result_recovery_components_test.cpp" />
+    <ClCompile Include="..\tests\unit\results\result_recovery_test.cpp" />
+    <ClCompile Include="..\tests\unit\results\results_writer_test.cpp" />
+    <ClCompile Include="..\tests\unit\solvers\eigen\mkl_feast_eigen_solver_test.cpp" />
+    <ClCompile Include="..\tests\unit\solvers\linear\linear_solver_test.cpp" />
+    <ClCompile Include="..\tests\unit\solvers\linear\mkl_pardiso_solver_test.cpp" />
+    <ClCompile Include="..\tests\unit\solvers\linear\tangent_solver_test.cpp" />
+  </ItemGroup>
+  <ItemGroup>
+    <ProjectReference Include="fesa_solver.vcxproj"><Project>{3AEC39D9-4641-5161-9107-265EB50CA882}</Project><LinkLibraryDependencies>true</LinkLibraryDependencies></ProjectReference>
+    <ProjectReference Include="gtest.vcxproj"><Project>{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}</Project><LinkLibraryDependencies>true</LinkLibraryDependencies></ProjectReference>
+  </ItemGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
+  <Import Project="Fesa.Runtime.targets" />
+</Project>

msvc/gtest.vcxproj

@@ -0,0 +1,19 @@
+<?xml version="1.0" encoding="utf-8"?>
+<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup Label="ProjectConfigurations"><ProjectConfiguration Include="Debug|x64"><Configuration>Debug</Configuration><Platform>x64</Platform></ProjectConfiguration><ProjectConfiguration Include="Release|x64"><Configuration>Release</Configuration><Platform>x64</Platform></ProjectConfiguration></ItemGroup>
+  <PropertyGroup Label="Globals"><ProjectGuid>{03194BA4-3F3B-5399-BCAF-FB4FA47300CE}</ProjectGuid><Keyword>Win32Proj</Keyword><WindowsTargetPlatformVersion>10.0</WindowsTargetPlatformVersion></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
+  <PropertyGroup Label="Configuration"><ConfigurationType>StaticLibrary</ConfigurationType><PlatformToolset>v145</PlatformToolset><UseDebugLibraries Condition="'$(Configuration)'=='Debug'">true</UseDebugLibraries></PropertyGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
+  <Import Project="Fesa.Common.props" />
+
+  <ItemGroup>
+    <ClCompile Include="$(FESA_GTEST_SOURCE_DIR)\googletest\src\gtest-all.cc" />
+    <ClCompile Include="$(FESA_GTEST_SOURCE_DIR)\googletest\src\gtest_main.cc" />
+  </ItemGroup>
+  <ItemGroup>
+
+  </ItemGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
+  <Import Project="Fesa.Runtime.targets" />
+</Project>

src/fesa/CMakeLists.txt

@@ -41,6 +41,7 @@ add_library(
     core/ascii.cpp
     core/diagnostic.cpp
     core/status.cpp
+    elements/element_capabilities.cpp
     elements/element_factory.cpp
     elements/hex8_element.cpp
     elements/hex8_high_low.cpp
@@ -93,12 +94,14 @@ add_library(
     results/analysis_state_commit.cpp
     results/beam_result_recovery.cpp
     results/global_equilibrium_recovery.cpp
+    results/prepared_results_writer.cpp
     results/recovery_candidate.cpp
     results/result_recovery.cpp
     results/shell_result_recovery.cpp
     solvers/eigen/mkl_feast_eigen_solver.cpp
     solvers/linear/mkl_pardiso_solver.cpp
     solvers/linear/mkl_pardiso_tangent_solver.cpp
+    solvers/linear/pardiso_session.cpp
 )
 
 target_include_directories(

src/fesa/analysis/analysis_procedures.h

@@ -0,0 +1,170 @@
+#ifndef FESA_ANALYSIS_ANALYSIS_PROCEDURES_H_
+#define FESA_ANALYSIS_ANALYSIS_PROCEDURES_H_
+
+#include "fesa/analysis/analysis_procedure.h"
+#include "fesa/analysis/hht_dynamic_procedure.h"
+#include "fesa/analysis/linear_frequency_procedure.h"
+#include "fesa/analysis/linear_static_procedure.h"
+#include "fesa/analysis/nonlinear_static_procedure.h"
+#include "fesa/analysis/prepared_analysis_outcome.h"
+#include "fesa/analysis/solid_frequency_procedure.h"
+#include "fesa/analysis/solid_hht_dynamic_procedure.h"
+#include "fesa/analysis/solid_static_procedure.h"
+#include "fesa/analysis/transient_heat_procedure.h"
+
+namespace fesa {
+
+class EigenSolver;
+
+/// @brief Adapts the LinearStatic lifecycle to prepared execution.
+/// @note Referenced backend and log adapters must outlive this procedure.
+class LinearStaticProcedure final : public AnalysisProcedure {
+ public:
+  /// @brief Injects only the adapters required by this family.
+  LinearStaticProcedure(const ParallelFor& parallel_for,
+                        LinearSolver& linear_solver)
+      : executor_(parallel_for, linear_solver) {}
+  /// @brief Retains compatibility with an already configured typed executor.
+  explicit LinearStaticProcedure(LinearStaticProcedureExecutor executor)
+      : executor_(executor) {}
+  Result<PreparedAnalysisOutcome> Execute(const Domain& domain) override;
+
+ private:
+  LinearStaticProcedureExecutor executor_;
+};
+
+/// @brief Adapts the NonlinearStatic lifecycle to prepared execution.
+/// @note Referenced backend and log adapters must outlive this procedure.
+class NonlinearStaticProcedure final : public AnalysisProcedure {
+ public:
+  /// @brief Injects only the adapters required by this family.
+  NonlinearStaticProcedure(const ParallelFor& parallel_for,
+                           TangentSolver& tangent_solver,
+                           NewtonIterationLogWriter& log)
+      : executor_(parallel_for, tangent_solver), log_(log) {}
+  /// @brief Retains compatibility with an already configured typed executor.
+  explicit NonlinearStaticProcedure(NonlinearStaticProcedureExecutor executor,
+                                    NewtonIterationLogWriter& log)
+      : executor_(executor), log_(log) {}
+  Result<PreparedAnalysisOutcome> Execute(const Domain& domain) override;
+
+ private:
+  NonlinearStaticProcedureExecutor executor_;
+  NewtonIterationLogWriter& log_;
+};
+
+/// @brief Adapts the LinearFrequency lifecycle to prepared execution.
+/// @note Referenced backend and log adapters must outlive this procedure.
+class LinearFrequencyProcedure final : public AnalysisProcedure {
+ public:
+  /// @brief Injects only the adapters required by this family.
+  LinearFrequencyProcedure(const EigenSolver& eigen_solver)
+      : executor_(eigen_solver) {}
+  /// @brief Retains compatibility with an already configured typed executor.
+  explicit LinearFrequencyProcedure(LinearFrequencyProcedureExecutor executor)
+      : executor_(executor) {}
+  Result<PreparedAnalysisOutcome> Execute(const Domain& domain) override;
+
+ private:
+  LinearFrequencyProcedureExecutor executor_;
+};
+
+/// @brief Adapts the HhtDynamic lifecycle to prepared execution.
+/// @note Referenced backend and log adapters must outlive this procedure.
+class HhtDynamicProcedure final : public AnalysisProcedure {
+ public:
+  /// @brief Injects only the adapters required by this family.
+  HhtDynamicProcedure(const ParallelFor& parallel_for,
+                      LinearSolver& positive_solver,
+                      TangentSolver& tangent_solver,
+                      NewtonIterationLogWriter& log)
+      : executor_(parallel_for, positive_solver, tangent_solver), log_(log) {}
+  /// @brief Retains compatibility with an already configured typed executor.
+  explicit HhtDynamicProcedure(HhtDynamicProcedureExecutor executor,
+                               NewtonIterationLogWriter& log)
+      : executor_(executor), log_(log) {}
+  Result<PreparedAnalysisOutcome> Execute(const Domain& domain) override;
+
+ private:
+  HhtDynamicProcedureExecutor executor_;
+  NewtonIterationLogWriter& log_;
+};
+
+/// @brief Adapts the SolidStatic lifecycle to prepared execution.
+/// @note Referenced backend and log adapters must outlive this procedure.
+class SolidStaticProcedure final : public AnalysisProcedure {
+ public:
+  /// @brief Injects only the adapters required by this family.
+  SolidStaticProcedure(const ParallelFor& parallel_for,
+                       LinearSolver& linear_solver,
+                       TangentSolver& tangent_solver,
+                       NewtonIterationLogWriter& log)
+      : executor_(parallel_for, linear_solver, tangent_solver), log_(log) {}
+  /// @brief Retains compatibility with an already configured typed executor.
+  explicit SolidStaticProcedure(SolidStaticProcedureExecutor executor,
+                                NewtonIterationLogWriter& log)
+      : executor_(executor), log_(log) {}
+  Result<PreparedAnalysisOutcome> Execute(const Domain& domain) override;
+
+ private:
+  SolidStaticProcedureExecutor executor_;
+  NewtonIterationLogWriter& log_;
+};
+
+/// @brief Adapts the SolidFrequency lifecycle to prepared execution.
+/// @note Referenced backend and log adapters must outlive this procedure.
+class SolidFrequencyProcedure final : public AnalysisProcedure {
+ public:
+  /// @brief Injects only the adapters required by this family.
+  SolidFrequencyProcedure(const EigenSolver& eigen_solver)
+      : executor_(eigen_solver) {}
+  /// @brief Retains compatibility with an already configured typed executor.
+  explicit SolidFrequencyProcedure(SolidFrequencyProcedureExecutor executor)
+      : executor_(executor) {}
+  Result<PreparedAnalysisOutcome> Execute(const Domain& domain) override;
+
+ private:
+  SolidFrequencyProcedureExecutor executor_;
+};
+
+/// @brief Adapts the SolidHhtDynamic lifecycle to prepared execution.
+/// @note Referenced backend and log adapters must outlive this procedure.
+class SolidHhtDynamicProcedure final : public AnalysisProcedure {
+ public:
+  /// @brief Injects only the adapters required by this family.
+  SolidHhtDynamicProcedure(const ParallelFor& parallel_for,
+                           LinearSolver& positive_solver,
+                           TangentSolver& tangent_solver,
+                           NewtonIterationLogWriter& log)
+      : executor_(parallel_for, positive_solver, tangent_solver), log_(log) {}
+  /// @brief Retains compatibility with an already configured typed executor.
+  explicit SolidHhtDynamicProcedure(SolidHhtDynamicProcedureExecutor executor,
+                                    NewtonIterationLogWriter& log)
+      : executor_(executor), log_(log) {}
+  Result<PreparedAnalysisOutcome> Execute(const Domain& domain) override;
+
+ private:
+  SolidHhtDynamicProcedureExecutor executor_;
+  NewtonIterationLogWriter& log_;
+};
+
+/// @brief Adapts the TransientHeat lifecycle to prepared execution.
+/// @note Referenced backend and log adapters must outlive this procedure.
+class TransientHeatProcedure final : public AnalysisProcedure {
+ public:
+  /// @brief Injects only the adapters required by this family.
+  TransientHeatProcedure(const ParallelFor& parallel_for,
+                         LinearSolver& linear_solver)
+      : executor_(parallel_for, linear_solver) {}
+  /// @brief Retains compatibility with an already configured typed executor.
+  explicit TransientHeatProcedure(TransientHeatProcedureExecutor executor)
+      : executor_(executor) {}
+  Result<PreparedAnalysisOutcome> Execute(const Domain& domain) override;
+
+ private:
+  TransientHeatProcedureExecutor executor_;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_ANALYSIS_PROCEDURES_H_

src/fesa/analysis/analysis_state.cpp

@@ -7,9 +7,15 @@
 #include <string>
 #include <utility>
 
+#include "fesa/fem/dof_manager.h"
+#include "math/finite_values.h"
+#include "results/shell_result_recovery.h"
+
 namespace fesa {
 namespace {
 
+using math_internal::IsFinite;
+
 constexpr std::size_t kShellLocationsPerElement = 4U;
 
 /// @brief Creates a structured failure without mutating existing state.
@@ -21,31 +27,6 @@ Status ShellCandidateFailure(const std::string& code,
       {{Severity::kError, code, {}, "ANALYSIS_STATE", identity, message}});
 }
 
-template <std::size_t Size>
-/// @brief Tests one fixed-size candidate component array for finite values.
-bool IsFinite(const std::array<double, Size>& values) {
-  return std::all_of(values.begin(), values.end(),
-                     [](const double value) { return std::isfinite(value); });
-}
-
-/// @brief Tests every physical shell row component for finite values.
-bool IsFinite(const ShellResultRow& row) {
-  if (!IsFinite(row.natural_coordinates) || !IsFinite(row.generalized_strain) ||
-      !IsFinite(row.section_resultant)) {
-    return false;
-  }
-  for (const auto& axis : row.local_frame) {
-    if (!IsFinite(axis)) {
-      return false;
-    }
-  }
-  return std::all_of(row.stress.begin(), row.stress.end(),
-                     [](const ShellSectionStressRow& stress) {
-                       return std::isfinite(stress.zeta) &&
-                              IsFinite(stress.components);
-                     });
-}
-
 }  // namespace
 
 AnalysisState AnalysisState::Create(const DofManager& dofs,
@@ -170,7 +151,7 @@ Status AnalysisState::CommitShellResults(
               "Shell stress rows require BOTTOM, MIDDLE, TOP identity.");
         }
       }
-      if (!IsFinite(row)) {
+      if (!results_internal::IsFiniteShellRow(row)) {
         return ShellCandidateFailure(
             "nonfinite-shell-state-value", std::to_string(row.element),
             "Shell result rows must contain only finite values.");

src/fesa/analysis/dynamic_analysis_state.cpp

@@ -1,18 +1,24 @@
 #include "fesa/analysis/dynamic_analysis_state.h"
 
-#include <algorithm>
 #include <cmath>
 #include <limits>
 #include <stdexcept>
 #include <string>
 #include <utility>
 
+#include "fesa/core/source_identity.h"
 #include "fesa/elements/element_definition.h"
 #include "fesa/elements/finite_rotation.h"
+#include "math/finite_values.h"
+#include "results/shell_result_recovery.h"
+#include "analysis/shell_state_inventory.h"
 
 namespace fesa {
 namespace {
 
+using analysis_internal::ShellElementOrder;
+using math_internal::IsFinite;
+
 constexpr std::size_t kDofsPerNode = 6U;
 constexpr std::size_t kAngularDofsPerNode = 3U;
 constexpr std::size_t kShellLocationsPerElement = 4U;
@@ -28,59 +34,6 @@ Status Failure(const FailureCategory category, const std::string& message) {
                                      message}});
 }
 
-/// @brief Compares canonical and raw source identity exactly.
-bool SameId(const SourceEntityId& left, const SourceEntityId& right) {
-  return left.instance_name == right.instance_name &&
-         left.source_label == right.source_label &&
-         left.source_label_text == right.source_label_text;
-}
-
-/// @brief Checks all components of one fixed-size physical record.
-template <std::size_t Size>
-bool IsFinite(const std::array<double, Size>& values) {
-  return std::all_of(values.begin(), values.end(),
-                     [](double value) { return std::isfinite(value); });
-}
-
-/// @brief Checks every vector component before state acceptance.
-bool IsFinite(const Vector& values) {
-  for (std::size_t index = 0U; index < values.Size(); ++index) {
-    if (!std::isfinite(values[index])) {
-      return false;
-    }
-  }
-  return true;
-}
-
-/// @brief Checks all physical recovery quantities for finite values.
-bool IsFinite(const ShellResultRow& row) {
-  if (!IsFinite(row.natural_coordinates) || !IsFinite(row.generalized_strain) ||
-      !IsFinite(row.section_resultant)) {
-    return false;
-  }
-  for (const auto& axis : row.local_frame) {
-    if (!IsFinite(axis)) {
-      return false;
-    }
-  }
-  return std::all_of(row.stress.begin(), row.stress.end(),
-                     [](const ShellSectionStressRow& stress) {
-                       return std::isfinite(stress.zeta) &&
-                              IsFinite(stress.components);
-                     });
-}
-
-/// @brief Collects stable Domain indices for recovery identity.
-std::vector<EntityIndex> ShellElementOrder(const Domain& domain) {
-  std::vector<EntityIndex> order;
-  for (std::size_t index = 0U; index < domain.Elements().Size(); ++index) {
-    if (domain.Elements()[index].Kind() == ElementDefinitionKind::kMitc4Shell) {
-      order.push_back(static_cast<EntityIndex>(index));
-    }
-  }
-  return order;
-}
-
 /// @brief Requires complete ordered Gauss and section-position rows.
 Status ValidateShellRows(const DynamicAcceptedFrameState& frame,
                          const std::vector<EntityIndex>& shell_order) {
@@ -110,7 +63,7 @@ Status ValidateShellRows(const DynamicAcceptedFrameState& frame,
           frame.shell_results[element * kShellLocationsPerElement + point];
       if (row.element != shell_order[element] ||
           row.location != kLocations[point] ||
-          row.natural_coordinates != natural[point] || !IsFinite(row)) {
+          row.natural_coordinates != natural[point] || !results_internal::IsFiniteShellRow(row)) {
         return Failure(FailureCategory::kSolver,
                        "Shell recovery rows have invalid identity or values.");
       }
@@ -228,7 +181,7 @@ Status DynamicAnalysisState::CommitAcceptedFrame(
   }
   for (std::size_t node = 0U; node < node_count; ++node) {
     if (frame.nodal_internal_order[node] != node ||
-        !SameId(frame.nodal_source_ids[node], nodal_source_ids_[node]) ||
+        !SourceIdentityEquals(frame.nodal_source_ids[node], nodal_source_ids_[node]) ||
         !IsFinite(frame.nodal_triad[node][0U]) ||
         !IsFinite(frame.nodal_triad[node][1U]) ||
         !IsFinite(frame.nodal_triad[node][2U]) ||

src/fesa/analysis/eigen_reduction.cpp

@@ -162,54 +162,49 @@ Result<NodalLift> MakeLift(const Matrix& mass,
             Failure("eigen-mass-conditioning", node,
                     "A positive-space mass pivot is not resolvable."));
     }
-  Matrix lower(positive, positive);
-  Matrix inverse_lower(positive, positive);
-  if (!dense_blas_internal::CholeskyLowerAndInverse(normalized_mp, lower,
-                                                  inverse_lower)) {
+  const auto factor = dense_blas_internal::DenseFactor::Cholesky(normalized_mp);
+  if (!factor.HasValue()) {
     return Result<NodalLift>::Failure(
         Failure("eigen-mass-conditioning", node,
                 "A positive-space mass pivot is not resolvable."));
   }
+  const Matrix lower = std::move(factor.Value().Lower().Value());
   Matrix transposed_lower(positive, positive);
-  Matrix scaled_inverse_transpose(positive, positive);
-  const double root_scale = std::sqrt(scale);
   for (std::size_t i = 0; i < positive; ++i)
-    for (std::size_t j = 0; j < positive; ++j) {
+    for (std::size_t j = 0; j < positive; ++j)
       transposed_lower(i, j) = lower(j, i);
-      scaled_inverse_transpose(i, j) = inverse_lower(j, i) / root_scale;
-    }
-  const auto inverse_mass = dense_blas_internal::MultiplyTransposeLeft(
-      inverse_lower, inverse_lower);
+  const auto condition = factor.Value().ReciprocalConditionInfinity();
   const auto rebuilt_mass = lower.Multiply(transposed_lower);
-  double norm_mp = 0.0;
-  double norm_inverse = 0.0;
   double reconstruction = 0.0;
   double scaled_mass_norm = 0.0;
   double rebuilt_mass_norm = 0.0;
   for (std::size_t i = 0; i < positive; ++i) {
-    double row_mp = 0.0;
-    double row_inverse = 0.0;
     for (std::size_t j = 0; j < positive; ++j) {
-      const double inverse = inverse_mass(i, j);
       const double rebuilt = rebuilt_mass(i, j);
-      row_inverse += std::abs(inverse);
-      row_mp += std::abs(mp(i, j) / scale);
       reconstruction = std::hypot(reconstruction, rebuilt - mp(i, j) / scale);
       scaled_mass_norm = std::hypot(scaled_mass_norm, mp(i, j) / scale);
       rebuilt_mass_norm = std::hypot(rebuilt_mass_norm, rebuilt);
     }
-    norm_mp = (std::max)(norm_mp, row_mp);
-    norm_inverse = (std::max)(norm_inverse, row_inverse);
   }
-  result.record.rcond_inf = (1.0 / norm_mp) / norm_inverse;
-  if (!(result.record.rcond_inf >= kConditionLimit) ||
+  if (!condition.HasValue() || !(condition.Value() >= kConditionLimit) ||
       !(Ratio(reconstruction, scaled_mass_norm + rebuilt_mass_norm) <=
         kAlgebraLimit)) {
     return Result<NodalLift>::Failure(Failure(
         "eigen-mass-conditioning", node,
         "Nodal mass fails rcond_inf >= 2^-32 or Cholesky reconstruction."));
   }
-  result.scaled_lift = basis.Multiply(scaled_inverse_transpose);
+  result.record.rcond_inf = condition.Value();
+  // X L^T = basis/sqrt(scale), so X^T M_scaled X = I.
+  Matrix scaled_basis = basis;
+  const double root_scale = std::sqrt(scale);
+  for (std::size_t c = 0; c < 6U; ++c)
+    for (std::size_t j = 0; j < positive; ++j)
+      scaled_basis(c, j) /= root_scale;
+  auto whitened = factor.Value().SolveLowerRight(scaled_basis, true);
+  if (!whitened.HasValue())
+    return Result<NodalLift>::Failure(Failure(
+        "eigen-mass-conditioning", node, "Nodal whitening is nonfinite."));
+  result.scaled_lift = std::move(whitened.Value());
   for (std::size_t c = 0; c < 6U; ++c) {
     for (std::size_t j = 0; j < positive; ++j) {
       if (!std::isfinite(result.scaled_lift(c, j))) {

src/fesa/analysis/equilibrium_algorithm.h

@@ -0,0 +1,86 @@
+#ifndef FESA_ANALYSIS_EQUILIBRIUM_ALGORITHM_H_
+#define FESA_ANALYSIS_EQUILIBRIUM_ALGORITHM_H_
+
+#include <cstdint>
+#include <functional>
+#include <optional>
+#include <utility>
+
+#include "fesa/core/status.h"
+
+namespace fesa {
+
+/// @brief Controls evaluated iteration order without owning a family candidate.
+/// @note Evaluation and its referenced trial context remain alive and unmoved
+/// throughout this call. A successful evaluation value means candidate ready.
+class EquilibriumAlgorithm {
+ public:
+  using Evaluation = std::function<Result<bool>(std::uint32_t)>;
+  virtual ~EquilibriumAlgorithm() = default;
+  virtual Status SolveCurrentStep(std::uint32_t first, std::uint32_t last,
+                                  const Evaluation& evaluate) = 0;
+};
+
+/// @brief Preserves the original inclusive full-Newton evaluation sequence.
+class NewtonStepAlgorithm final : public EquilibriumAlgorithm {
+ public:
+  Status SolveCurrentStep(std::uint32_t first, std::uint32_t last,
+                          const Evaluation& evaluate) override {
+    for (std::uint32_t iteration = first; iteration <= last; ++iteration) {
+      auto result = evaluate(iteration);
+      if (!result.HasValue()) return result.GetStatus();
+      if (result.Value()) return Status::Ok();
+    }
+    // Family evaluators retain their original final-evaluation failure.
+    return Status::Ok();
+  }
+};
+
+/// @brief Owns one procedure-local typed evaluator and unpublished candidate.
+/// @note This value is not an algorithm interface. The injected algorithm never
+/// owns or type-erases Candidate, and neither callback nor context may escape.
+template <typename Candidate, std::uint32_t kFirstIteration>
+class EquilibriumStep {
+ public:
+  using Evaluation =
+      std::function<Result<std::optional<Candidate>>(std::uint32_t)>;
+  EquilibriumStep(Evaluation evaluate, std::uint32_t maximum)
+      : evaluate_(std::move(evaluate)), maximum_(maximum) {}
+  EquilibriumStep(const EquilibriumStep&) = delete;
+  EquilibriumStep& operator=(const EquilibriumStep&) = delete;
+  Status Solve(EquilibriumAlgorithm& algorithm) {
+    const EquilibriumAlgorithm::Evaluation evaluate =
+        [this](std::uint32_t iteration) -> Result<bool> {
+      auto result = evaluate_(iteration);
+      if (!result.HasValue()) return Result<bool>::Failure(result.GetStatus());
+      if (result.Value().has_value()) {
+        pending_ = std::move(result.Value());
+        return Result<bool>::Success(true);
+      }
+      return Result<bool>::Success(false);
+    };
+    return algorithm.SolveCurrentStep(kFirstIteration, maximum_, evaluate);
+  }
+  bool HasCandidate() const { return pending_.has_value(); }
+  /// @brief Transfers the validated candidate to the procedure commit boundary.
+  Candidate TakeCandidate() { return std::move(pending_.value()); }
+
+ private:
+  Evaluation evaluate_;
+  std::uint32_t maximum_;
+  std::optional<Candidate> pending_;
+};
+
+// Static evaluations start at one; mechanical HHT corrections start at zero.
+// Evaluation at the maximum still performs the existing endpoint validation.
+template <typename Candidate>
+using ShellFullNewtonStep = EquilibriumStep<Candidate, 1U>;
+template <typename Candidate>
+using SolidFullNewtonStep = EquilibriumStep<Candidate, 1U>;
+template <typename Candidate>
+using ReducedShellHhtStep = EquilibriumStep<Candidate, 0U>;
+template <typename Candidate>
+using SolidHhtStep = EquilibriumStep<Candidate, 0U>;
+
+}  // namespace fesa
+#endif  // FESA_ANALYSIS_EQUILIBRIUM_ALGORITHM_H_

src/fesa/analysis/hht_dynamic_algebra.cpp

@@ -16,11 +16,14 @@
 #include "fesa/solvers/linear/linear_solver.h"
 #include "fesa/solvers/linear/tangent_solver.h"
 #include "math/dense_blas_internal.h"
+#include "math/compensated_sum.h"
 
 namespace fesa {
 namespace hht_internal {
 namespace {
 
+using math_internal::AddCompensated;
+
 /// @brief Attaches a fail-closed dynamic diagnostic to the source model.
 Status Failure(const Domain& domain, const std::string& code,
                const std::string& message) {
@@ -148,48 +151,23 @@ Status CheckLocalMass(const Domain& domain, const SparseMatrix& matrix,
     return Failure(domain, "dynamic-positive-mass",
                    "A nonempty physical mass block has no positive scale.");
   }
-  double norm = 0.0;
-  for (std::size_t i = 0; i < size; ++i) {
-    double sum = 0.0;
-    for (std::size_t j = 0; j < size; ++j) {
-      block(i, j) /= scale;
-      sum += std::abs(block(i, j));
-    }
-    norm = std::max(norm, sum);
-  }
-  Matrix lower{size, size};
-  Matrix inverse_lower{size, size};
-  auto factor_failure = dense_blas_internal::CholeskyFailure::kNone;
+  for (std::size_t i = 0; i < size; ++i)
+    for (std::size_t j = 0; j < size; ++j) block(i, j) /= scale;
   try {
-    if (!dense_blas_internal::CholeskyLowerAndInverse(
-            block, lower, inverse_lower, &factor_failure)) {
-      if (factor_failure == dense_blas_internal::CholeskyFailure::kInverse)
-        return Failure(
-            domain, "dynamic-positive-mass-conditioning",
-            "A nodal free physical block reciprocal condition is below 2^-32.");
+    const auto factor = dense_blas_internal::DenseFactor::Cholesky(block);
+    if (!factor.HasValue())
       return Failure(
           domain, "dynamic-positive-mass",
           "Physical mass requires strictly positive Cholesky pivots.");
-    }
+    const auto rcond = factor.Value().ReciprocalConditionInfinity();
+    if (!rcond.HasValue() || !std::isfinite(rcond.Value()) ||
+        !(rcond.Value() >= std::ldexp(1.0, -32)))
+      return Failure(
+          domain, "dynamic-positive-mass-conditioning",
+          "A nodal free physical block reciprocal condition is below 2^-32.");
   } catch (const std::exception& error) {
     return Failure(domain, "dynamic-positive-mass", error.what());
   }
-  const Matrix inverse =
-      dense_blas_internal::MultiplyTransposeLeft(inverse_lower, inverse_lower);
-  std::array<double, 6> sums{};
-  for (std::size_t column = 0; column < size; ++column) {
-    for (std::size_t i = 0; i < size; ++i) {
-      sums[i] += std::abs(inverse(i, column));
-    }
-  }
-  const double inverse_norm = *std::max_element(sums.begin(), sums.end());
-  const double rcond = 1.0 / norm / inverse_norm;
-  if (!std::isfinite(inverse_norm) || !std::isfinite(rcond) ||
-      !(rcond >= std::ldexp(1.0, -32))) {
-    return Failure(
-        domain, "dynamic-positive-mass-conditioning",
-        "A nodal free physical block reciprocal condition is below 2^-32.");
-  }
   return Status::Ok();
 }
 
@@ -468,15 +446,6 @@ Result<SparseMatrix> ConstraintGradient(const DynamicAssembly& assembly,
                     std::move(entries));
 }
 
-/// @brief Accumulates one deterministic sparse contraction without lost sums.
-void AddCompensated(const double term, double* sum, double* correction) {
-  const double next = *sum + term;
-  *correction += std::abs(*sum) >= std::abs(term)
-                     ? (*sum - next) + term
-                     : (term - next) + *sum;
-  *sum = next;
-}
-
 /// @brief Stores W-scaled regularity with exact inverse-action infinity norms.
 struct Regularity {
   SparseMatrix matrix;
@@ -553,23 +522,10 @@ Result<Regularity> CheckRegularity(const Domain& domain,
       sum += std::abs(matrix.Value().Values()[index]);
     norm = std::max(norm, sum);
   }
-  Vector inverse_sums{nodes.size()};
-  // Columns are discarded after their absolute row sums are accumulated;
-  // a global dense inverse is never retained.
-  for (std::size_t column = 0; column < nodes.size(); ++column) {
-    Vector rhs{nodes.size()};
-    rhs[column] = 1.0;
-    Vector solution{nodes.size()};
-    const Status solved = solver.SolveCorrection(rhs, solution);
-    if (!solved.IsOk()) return Result<Regularity>::Failure(solved);
-    const Status checked = CheckLinearSolve(matrix.Value(), rhs, solution);
-    if (!checked.IsOk()) return Result<Regularity>::Failure(checked);
-    for (std::size_t row = 0; row < nodes.size(); ++row)
-      inverse_sums[row] += std::abs(solution[row]);
-  }
   double inverse_norm = 0.0;
-  for (std::size_t row = 0; row < nodes.size(); ++row)
-    inverse_norm = std::max(inverse_norm, inverse_sums[row]);
+  const Status accumulated =
+      AccumulateCheckedCanonicalNorm(matrix.Value(), solver, inverse_norm);
+  if (!accumulated.IsOk()) return Result<Regularity>::Failure(accumulated);
   const double condition = 1.0 / norm / inverse_norm;
   if (!std::isfinite(norm) || !std::isfinite(inverse_norm) ||
       !std::isfinite(condition) || !(condition >= std::ldexp(1.0, -32))) {
@@ -662,6 +618,26 @@ Status HiddenEvidence(const Domain& domain, const DynamicAssembly& assembly,
 
 }  // namespace
 
+Status AccumulateCheckedCanonicalNorm(const SparseMatrix& matrix,
+                                      TangentSolver& solver, double& norm) {
+  const auto size = matrix.Rows();
+  Vector row_sums{size};
+  for (std::size_t column = 0U; column < size; ++column) {
+    Vector rhs{size};
+    rhs[column] = 1.0;
+    Vector solution{size};
+    const Status solved = solver.SolveCorrection(rhs, solution);
+    if (!solved.IsOk()) return solved;
+    const Status checked = CheckLinearSolve(matrix, rhs, solution);
+    if (!checked.IsOk()) return checked;
+    for (std::size_t row = 0U; row < size; ++row)
+      row_sums[row] += std::abs(solution[row]);
+  }
+  for (std::size_t row = 0U; row < size; ++row)
+    norm = (std::max)(norm, row_sums[row]);
+  return Status::Ok();
+}
+
 double OrderedNullMetric(const SparseMatrix& metric, const std::size_t node,
                          const Vector3& direction) {
   Vector left{9U};

src/fesa/analysis/hht_dynamic_assembly.cpp

@@ -151,9 +151,24 @@ Result<std::vector<RuntimeShell>> BuildRuntimeShells(const Domain& domain,
                                                  *material, density);
     if (!inertia.HasValue())
       return Result<std::vector<RuntimeShell>>::Failure(inertia.GetStatus());
-    shells.push_back({static_cast<EntityIndex>(index),
-                      dofs.ShellElementScatter(static_cast<EntityIndex>(index)),
-                      std::move(internal.Value()), std::move(inertia.Value())});
+    auto internal_kernel =
+        std::make_unique<NonlinearMitc4Shell>(std::move(internal.Value()));
+    auto inertia_kernel =
+        std::make_unique<NonlinearMitc4Inertia>(std::move(inertia.Value()));
+    ElementDofLayout layout{
+        definition->SourceId(), definition->NodeIndices(),
+        {DofComponent::kUx, DofComponent::kUy, DofComponent::kUz,
+         DofComponent::kUrx, DofComponent::kUry, DofComponent::kUrz}};
+    auto trial = std::make_unique<Mitc4TrialAdapter>(layout, *internal_kernel);
+    auto kinetic = std::make_unique<Mitc4InertiaAdapter>(layout, *inertia_kernel);
+    auto mapped = dofs.ElementScatter(kinetic->DofLayout());
+    if (!mapped.HasValue())
+      return Result<std::vector<RuntimeShell>>::Failure(mapped.GetStatus());
+    std::array<std::size_t, 24> scatter{};
+    std::copy(mapped.Value().begin(), mapped.Value().end(), scatter.begin());
+    shells.push_back({static_cast<EntityIndex>(index), scatter,
+                      std::move(internal_kernel), std::move(inertia_kernel),
+                      std::move(trial), std::move(kinetic)});
   }
   return Result<std::vector<RuntimeShell>>::Success(std::move(shells));
 }
@@ -431,8 +446,8 @@ Result<DynamicAssembly> EvaluateAssembly(
     }
     const auto before = retain_constraints ? ReadTrialEvaluationContext()
                                            : TrialEvaluationContext{};
-    auto f = EvaluateInternalResidualAndTangent(
-        shells[e].internal, trial, directional_third ? &v : nullptr);
+    auto f = shells[e].internal->EvaluateTrial(
+        trial, directional_third ? &v : nullptr);
     if (!f.HasValue()) {
       failures[e] = f.GetStatus();
       return;
@@ -441,7 +456,7 @@ Result<DynamicAssembly> EvaluateAssembly(
       const auto after = ReadTrialEvaluationContext();
       if (ReusableTrialContext(before, after)) evaluation_contexts[e] = after;
     }
-    auto m = shells[e].inertia.Evaluate(trial, v, a);
+    auto m = shells[e].inertia->Evaluate(trial, v, a);
     if (!m.HasValue()) {
       failures[e] = m.GetStatus();
       return;
@@ -499,7 +514,7 @@ Result<DynamicAssembly> EvaluateAssembly(
           external_done[node] = true;
           const auto first = 6U * node + 3U;
           const auto external =
-              shells[e].internal.EvaluateExternalDrillingConstraint(
+              shells[e].internal->EvaluateExternalDrillingConstraint(
                   local, Triple(frame.generalized_coordinates, first),
                   Triple(frame.velocity, first),
                   Triple(frame.external_force, first), {}, {});
@@ -660,7 +675,7 @@ Result<DynamicAssembly> EvaluateAssembly(
       record.scatter = shells[e].scatter;
       record.configuration =
           nonlinear_mitc4_internal::ConfigurationSnapshot::Read(
-              shells[e].internal);
+              *shells[e].internal_kernel);
       record.evaluation_context = evaluation_contexts[e];
       for (std::size_t i = 0U; i < 24U; ++i) {
         record.q[i] = frame.generalized_coordinates[shells[e].scatter[i]];
@@ -703,11 +718,13 @@ Status CompleteEquilibrium(const Domain& domain, const DofManager& dofs,
     const auto first = 6U * node;
     const Vector3 arm = Vector3(domain.Nodes()[node].coordinates) +
                         Triple(frame->generalized_coordinates, first);
-    const Matrix transform = InverseTransposeLeftJacobianSO3(
-        Triple(frame->generalized_coordinates, first + 3U));
+    const Vector3 phi = Triple(frame->generalized_coordinates, first + 3U);
     for (const Vector* values : {&frame->external_force, &frame->reaction}) {
       const Vector3 force = Triple(*values, first);
-      const Vector3 moment = Transform(transform, Triple(*values, first + 3U));
+      const auto spatial = SpatialMomentSO3(phi, Triple(*values, first + 3U));
+      if (!spatial.HasValue())
+        return Failure("Dynamic physical force or moment balance exceeds 1e-8.");
+      const Vector3 moment = spatial.Value();
       total_force = total_force + force;
       total_moment = total_moment + arm.Cross(force) + moment;
       force_scale += force.Norm();

src/fesa/analysis/hht_dynamic_internal.h

@@ -4,11 +4,13 @@
 #include <array>
 #include <cstdint>
 #include <filesystem>
+#include <memory>
 #include <optional>
 #include <vector>
 
 #include "fesa/analysis/dynamic_analysis_state.h"
 #include "fesa/analysis/hht_time_integration.h"
+#include "fesa/elements/element_capabilities.h"
 #include "fesa/elements/nonlinear_mitc4_inertia.h"
 #include "fesa/elements/nonlinear_mitc4_shell.h"
 #include "fesa/math/sparse_matrix.h"
@@ -25,8 +27,10 @@ namespace hht_internal {
 struct RuntimeShell {
   EntityIndex element_index;
   std::array<std::size_t, 24> scatter;
-  NonlinearMitc4Shell internal;
-  NonlinearMitc4Inertia inertia;
+  std::unique_ptr<NonlinearMitc4Shell> internal_kernel;
+  std::unique_ptr<NonlinearMitc4Inertia> inertia_kernel;
+  std::unique_ptr<ShellTrialElement> internal;
+  std::unique_ptr<ShellInertiaElement> inertia;
 };
 
 /// @brief Captures only controls used by the current MSVC x64 local evaluator.
@@ -138,6 +142,12 @@ Result<SparseMatrix> ScaledFree(const SparseMatrix& matrix,
 Status CheckLinearSolve(const SparseMatrix& matrix, const Vector& rhs,
                         const Vector& solution);
 
+/// @brief Streams checked canonical solves into the caller's infinity norm.
+/// @note The caller owns factorization and the initial norm. Each column is
+/// discarded after ascending absolute row-sum accumulation; failures preserve norm.
+Status AccumulateCheckedCanonicalNorm(const SparseMatrix& matrix,
+                                      TangentSolver& solver, double& norm);
+
 /// @brief Finds analytic admissible node null directions without rank cuts.
 std::vector<std::size_t> NullNodes(
     const DofManager& dofs,

src/fesa/analysis/hht_reduced_integrator.h

@@ -0,0 +1,74 @@
+#ifndef FESA_ANALYSIS_HHT_REDUCED_INTEGRATOR_H_
+#define FESA_ANALYSIS_HHT_REDUCED_INTEGRATOR_H_
+#include <utility>
+#include "analysis/hht_reduced_internal.h"
+namespace fesa::hht_reduced_internal {
+struct ReducedHistory {
+  Vector p{0U};
+  Vector velocity{0U};
+  Vector acceleration{0U};
+  Vector algorithmic_acceleration{0U};
+  Vector z{0U};
+};
+
+/// @brief Keeps every private predictor compensation channel before a trial.
+struct ReducedShellPredictor {
+  Vector pp{0U};
+  Vector vpp{0U};
+  Vector coordinate_low{0U};
+  Vector increment_trace{0U};
+  Vector increment_trace_compensation{0U};
+  Vector increment_trace_absolute_sum{0U};
+};
+
+struct ReducedShellRateRequest {
+  const FixedChart& chart;
+  const ReducedHistory& history;
+  const Vector& trial_algorithmic;
+  const Vector& vpp;
+  bool copy_translation_rates;
+  const Vector& retained_velocity;
+  const Vector& retained_acceleration;
+  double h;
+  const HhtParameters& parameters;
+};
+
+struct ReducedShellTrialRates {
+  Vector velocity{0U};
+  Vector acceleration{0U};
+};
+
+/// @brief Handles private shell predictors and exact sparse rate
+/// reconstruction.
+/// @note Chart/root/solver are non-owning call views; no history is committed.
+class ShellHhtIntegrator {
+public:
+  virtual ~ShellHhtIntegrator() = default;
+  virtual ReducedShellPredictor
+  Predict(const ReducedHistory& history, double h,
+          const HhtParameters& parameters) const = 0;
+  /// @note Output buffers have history.p.Size() entries and do not alias any
+  /// request input or each other. The caller owns their allocation/lifetime.
+  virtual void EvaluateRates(const ReducedShellRateRequest& request,
+                              Vector& velocity, Vector& acceleration) const = 0;
+  virtual Result<ReconstructedRates>
+  ReconstructPhysicalRates(const FixedChart& chart, const EmbeddingRoot& root,
+                           const Vector& velocity, const Vector& acceleration,
+                           TangentSolver& solver) const = 0;
+};
+
+/// @brief Sequences one private predictor, pending endpoint and commit.
+/// @note Callables are synchronous borrowed views. They retain all original
+/// evaluation/diagnostic/commit policy; no accepted history is owned here.
+template <typename Evaluate, typename Commit>
+Status RunReducedHhtStep(const ShellHhtIntegrator& integrator,
+                         const ReducedHistory& history, double h,
+                         const HhtParameters& parameters,
+                         Evaluate&& evaluate, Commit&& commit) {
+  auto predictor = integrator.Predict(history, h, parameters);
+  auto pending = evaluate(integrator, std::move(predictor));
+  if (!pending.HasValue()) return pending.GetStatus();
+  return commit(std::move(pending.Value()));
+}
+}  // namespace fesa::hht_reduced_internal
+#endif  // FESA_ANALYSIS_HHT_REDUCED_INTEGRATOR_H_

src/fesa/analysis/hht_reduced_operators.cpp

@@ -10,13 +10,18 @@
 #include <string>
 #include <utility>
 
+#include "fesa/core/source_identity.h"
 #include "fesa/solvers/linear/tangent_solver.h"
 #include "math/dense_blas_internal.h"
 #include "math/high_low_arithmetic.h"
+#include "math/finite_values.h"
+#include "math/compensated_sum.h"
 
 namespace fesa::hht_reduced_internal {
 namespace {
 
+using RateSum = math_internal::CompensatedSum;
+
 Status Failure(const std::string& message,
                const std::string& code = "dynamic-invalid-state") {
   return Status::Failure(FailureCategory::kSolver,
@@ -25,27 +30,9 @@ Status Failure(const std::string& message,
 }
 
 bool Finite(const Vector& values) {
-  for (std::size_t i = 0U; i < values.Size(); ++i)
-    if (!std::isfinite(values[i])) return false;
-  return true;
+  return math_internal::IsFinite(values);
 }
 
-class RateSum {
- public:
-  void Add(const double term) {
-    const double next = sum_ + term;
-    correction_ += std::abs(sum_) >= std::abs(term)
-                       ? (sum_ - next) + term
-                       : (term - next) + sum_;
-    sum_ = next;
-  }
-  double Value() const { return sum_ + correction_; }
-
- private:
-  double sum_ = 0.0;
-  double correction_ = 0.0;
-};
-
 bool ExactlyEqual(const Vector& left, const Vector& right) {
   if (left.Size() != right.Size()) return false;
   for (std::size_t i = 0U; i < left.Size(); ++i)
@@ -65,13 +52,6 @@ bool SameBits(const double left, const double right) {
   return std::memcmp(&left, &right, sizeof(double)) == 0;
 }
 
-/// @brief Compares semantic and original source identity without object keys.
-bool SameSource(const SourceEntityId& left, const SourceEntityId& right) {
-  return left.instance_name == right.instance_name &&
-         left.source_label == right.source_label &&
-         left.source_label_text == right.source_label_text;
-}
-
 /// @brief Finds only the current complete directional response, otherwise miss.
 const hht_internal::DirectionalShellConstraintData* MatchingConstraints(
     const Domain& domain, const hht_internal::RuntimeShell& shell,
@@ -98,7 +78,7 @@ const hht_internal::DirectionalShellConstraintData* MatchingConstraints(
           hht_internal::ReadTrialEvaluationContext()))
     return nullptr;
   const auto configuration =
-      nonlinear_mitc4_internal::ConfigurationSnapshot::Read(shell.internal);
+      nonlinear_mitc4_internal::ConfigurationSnapshot::Read(*shell.internal_kernel);
   if (record.configuration.source.file != configuration.source.file ||
       record.configuration.source.line != configuration.source.line ||
       record.configuration.identity != configuration.identity)
@@ -116,7 +96,7 @@ const hht_internal::DirectionalShellConstraintData* MatchingConstraints(
   for (std::size_t node = 0U; node < 4U; ++node) {
     const auto global_node = shell.scatter[6U * node] / 6U;
     if (global_node >= domain.Nodes().size() ||
-        !SameSource(record.node_source_ids[node],
+        !SourceIdentityEquals(record.node_source_ids[node],
                     domain.Nodes()[global_node].source_id))
       return nullptr;
   }
@@ -534,7 +514,7 @@ Result<ConstraintOperators> EvaluateConstraintOperators(
     std::optional<NonlinearMitc4InternalEquilibrium> fresh;
     if (saved == nullptr) {
       auto internal =
-          EvaluateInternalResidualAndTangent(shell.internal, Trial(q), &v);
+          shell.internal->EvaluateTrial(Trial(q), &v);
       if (!internal.HasValue())
         return Result<ConstraintOperators>::Failure(internal.GetStatus());
       fresh = std::move(internal.Value());
@@ -572,7 +552,7 @@ Result<ConstraintOperators> EvaluateConstraintOperators(
       if (external_done[global_node]) continue;
       external_done[global_node] = true;
       const auto first = 6U * global_node + 3U;
-      const auto external = shell.internal.EvaluateExternalDrillingConstraint(
+      const auto external = shell.internal->EvaluateExternalDrillingConstraint(
           local_node, Vector3{q[6U * local_node + 3U],
                               q[6U * local_node + 4U],
                               q[6U * local_node + 5U]},
@@ -587,7 +567,7 @@ Result<ConstraintOperators> EvaluateConstraintOperators(
                   force_acceleration[first + 2U]});
       if (!external.HasValue())
         return Result<ConstraintOperators>::Failure(external.GetStatus());
-      const auto rate_term = shell.internal.EvaluateExternalDrillingConstraint(
+      const auto rate_term = shell.internal->EvaluateExternalDrillingConstraint(
           local_node, Vector3{q[6U * local_node + 3U],
                               q[6U * local_node + 4U],
                               q[6U * local_node + 5U]},
@@ -596,7 +576,7 @@ Result<ConstraintOperators> EvaluateConstraintOperators(
       if (!rate_term.HasValue())
         return Result<ConstraintOperators>::Failure(rate_term.GetStatus());
       const auto acceleration_term =
-          shell.internal.EvaluateExternalDrillingConstraint(
+          shell.internal->EvaluateExternalDrillingConstraint(
               local_node, Vector3{q[6U * local_node + 3U],
                                   q[6U * local_node + 4U],
                                   q[6U * local_node + 5U]},
@@ -1321,21 +1301,10 @@ Result<double> CheckGraphRegularity(
   if (!sparse.HasValue()) return Result<double>::Failure(sparse.GetStatus());
   Status status = solver.FactorizeFresh(sparse.Value());
   if (!status.IsOk()) return Result<double>::Failure(status);
-  Vector inverse_sums{size};
-  for (std::size_t column = 0U; column < size; ++column) {
-    Vector rhs{size};
-    rhs[column] = 1.0;
-    Vector solution{size};
-    status = solver.SolveCorrection(rhs, solution);
-    if (!status.IsOk()) return Result<double>::Failure(status);
-    status = hht_internal::CheckLinearSolve(sparse.Value(), rhs, solution);
-    if (!status.IsOk()) return Result<double>::Failure(status);
-    for (std::size_t row = 0U; row < size; ++row)
-      inverse_sums[row] += std::abs(solution[row]);
-  }
   double inverse_norm = 0.0;
-  for (std::size_t row = 0U; row < size; ++row)
-    inverse_norm = std::max(inverse_norm, inverse_sums[row]);
+  status = hht_internal::AccumulateCheckedCanonicalNorm(
+      sparse.Value(), solver, inverse_norm);
+  if (!status.IsOk()) return Result<double>::Failure(status);
   const double condition = 1.0 / norm / inverse_norm;
   if (!std::isfinite(norm) || !std::isfinite(inverse_norm) ||
       !std::isfinite(condition) || !(condition >= std::ldexp(1.0, -32))) {
@@ -1409,20 +1378,9 @@ Result<double> CheckSelectorTransversality(
     if (!sparse.HasValue()) return Result<double>::Failure(sparse.GetStatus());
     auto status = solver.FactorizeFresh(sparse.Value());
     if (!status.IsOk()) return Result<double>::Failure(status);
-    Vector inverse_rows{rows.size()};
-    for (std::size_t column = 0U; column < rows.size(); ++column) {
-      Vector rhs{rows.size()};
-      rhs[column] = 1.0;
-      Vector solution{rows.size()};
-      status = solver.SolveCorrection(rhs, solution);
-      if (!status.IsOk()) return Result<double>::Failure(status);
-      status = hht_internal::CheckLinearSolve(sparse.Value(), rhs, solution);
-      if (!status.IsOk()) return Result<double>::Failure(status);
-      for (std::size_t row = 0U; row < rows.size(); ++row)
-        inverse_rows[row] += std::abs(solution[row]);
-    }
-    for (std::size_t row = 0U; row < rows.size(); ++row)
-      inverse_norm = (std::max)(inverse_norm, inverse_rows[row]);
+    status = hht_internal::AccumulateCheckedCanonicalNorm(
+        sparse.Value(), solver, inverse_norm);
+    if (!status.IsOk()) return Result<double>::Failure(status);
   }
   const double condition = 1.0 / norm / inverse_norm;
   if (!std::isfinite(condition) || condition < std::ldexp(1.0, -32))

src/fesa/analysis/hht_reduced_procedure.cpp

@@ -1,4 +1,7 @@
 #include "analysis/hht_reduced_procedure.h"
+#include "analysis/hht_reduced_integrator.h"
+
+#include "equilibrium_algorithm.h"
 
 #include <algorithm>
 #include <cmath>
@@ -296,12 +299,83 @@ Status CheckReducedUpdates(const Domain& domain,
   return Status::Ok();
 }
 
-struct ReducedHistory {
-  Vector p{0U};
-  Vector velocity{0U};
-  Vector acceleration{0U};
-  Vector algorithmic_acceleration{0U};
-  Vector z{0U};
+// Private nonvirtual primitive: keep velocity assignment before acceleration
+// evaluation, including per-index position retries. No accepted state changes.
+void EvaluateReducedShellRate(double predictor_velocity,
+                              double algorithmic_acceleration,
+                              double old_acceleration, double h,
+                              const HhtParameters& parameters,
+                              double* velocity, double* acceleration) {
+  *velocity = predictor_velocity + parameters.gamma * h * algorithmic_acceleration;
+  *acceleration = (algorithmic_acceleration + parameters.alpha * old_acceleration) /
+                  (1.0 + parameters.alpha);
+}
+
+class ReducedCoordinateShellHhtIntegrator final : public ShellHhtIntegrator {
+public:
+  ReducedShellPredictor
+  Predict(const ReducedHistory& history, double h,
+          const HhtParameters& parameters) const override {
+    Vector pp{history.p.Size()}, vpp{history.p.Size()};
+    for (std::size_t i = 0U; i < history.p.Size(); ++i) {
+      pp[i] =
+          history.p[i] + h * history.velocity[i] +
+          h * h * (0.5 - parameters.beta) * history.algorithmic_acceleration[i];
+      vpp[i] = history.velocity[i] + h * (1.0 - parameters.gamma) *
+                                         history.algorithmic_acceleration[i];
+    }
+    Vector coordinate_low{history.p.Size()};
+    Vector increment_trace{history.p.Size()};
+    Vector increment_trace_compensation{history.p.Size()};
+    Vector increment_trace_absolute_sum{history.p.Size()};
+    for (std::size_t i = 0U; i < history.p.Size(); ++i) {
+      const double velocity_term = h * history.velocity[i];
+      const double old_acceleration_term =
+          h * h * (0.5 - parameters.beta) * history.algorithmic_acceleration[i];
+      const double first_sum = history.p[i] + velocity_term;
+      coordinate_low[i] =
+          AdditionLowPart(history.p[i], velocity_term, first_sum) +
+          AdditionLowPart(first_sum, old_acceleration_term, pp[i]);
+      AddIncrementTraceTerm(velocity_term, &increment_trace[i],
+                            &increment_trace_compensation[i]);
+      AddIncrementTraceTerm(old_acceleration_term, &increment_trace[i],
+                            &increment_trace_compensation[i]);
+      increment_trace_absolute_sum[i] =
+          std::abs(velocity_term) + std::abs(old_acceleration_term);
+    }
+    return {std::move(pp),
+            std::move(vpp),
+            std::move(coordinate_low),
+            std::move(increment_trace),
+            std::move(increment_trace_compensation),
+            std::move(increment_trace_absolute_sum)};
+  }
+  void EvaluateRates(const ReducedShellRateRequest& request,
+                      Vector& trial_v, Vector& trial_a) const override {
+    const auto& history = request.history;
+    const auto& trial_algorithmic = request.trial_algorithmic;
+    const auto& vpp = request.vpp;
+    const auto& parameters = request.parameters;
+    const double h = request.h;
+    for (std::size_t i = 0U; i < history.p.Size(); ++i) {
+      if (request.copy_translation_rates &&
+          PhysicalCoordinateChannel(request.chart, i) == 0U) {
+        trial_v[i] = request.retained_velocity[i];
+        trial_a[i] = request.retained_acceleration[i];
+      } else {
+        EvaluateReducedShellRate(
+            vpp[i], trial_algorithmic[i], history.acceleration[i], h, parameters,
+            &trial_v[i], &trial_a[i]);
+      }
+    }
+  }
+  Result<ReconstructedRates>
+  ReconstructPhysicalRates(const FixedChart& chart, const EmbeddingRoot& root,
+                           const Vector& velocity, const Vector& acceleration,
+                           TangentSolver& solver) const override {
+    return hht_reduced_internal::ReconstructPhysicalRates(chart, root, velocity,
+                                                          acceleration, solver);
+  }
 };
 
 struct Trial {
@@ -320,6 +394,17 @@ Result<DynamicExecutionResult> ExecuteReducedHht(
     const Domain& domain, NewtonIterationLogWriter& log,
     const ParallelFor& parallel_for, LinearSolver& positive_solver,
     TangentSolver& tangent_solver) {
+  const ReducedCoordinateShellHhtIntegrator integrator;
+  NewtonStepAlgorithm algorithm;
+  return ExecuteReducedHht(domain, log, parallel_for, positive_solver,
+                            tangent_solver, integrator, algorithm);
+}
+
+Result<DynamicExecutionResult> ExecuteReducedHht(
+    const Domain& domain, NewtonIterationLogWriter& log,
+    const ParallelFor& parallel_for, LinearSolver& positive_solver,
+    TangentSolver& tangent_solver, const ShellHhtIntegrator& integrator,
+    EquilibriumAlgorithm& algorithm) {
   if (domain.Dynamic() == nullptr)
     return Result<DynamicExecutionResult>::Failure(Status::Failure(
         FailureCategory::kModel, {{Severity::kError, "invalid-dynamic-step", {},
@@ -433,7 +518,7 @@ Result<DynamicExecutionResult> ExecuteReducedHht(
                                   tangent_solver);
   if (!root0.HasValue()) return Result<DynamicExecutionResult>::Failure(
       WithProcedureContext(domain, root0.GetStatus(), "inner-position", 0U, 0.0));
-  auto rates0 = ReconstructPhysicalRates(chart.Value(), root0.Value(), history.velocity,
+  auto rates0 = integrator.ReconstructPhysicalRates(chart.Value(), root0.Value(), history.velocity,
                                          history.acceleration, tangent_solver);
   if (!rates0.HasValue()) return Result<DynamicExecutionResult>::Failure(
       WithProcedureContext(domain, rates0.GetStatus(), "inner-rates", 0U, 0.0));
@@ -604,343 +689,434 @@ Result<DynamicExecutionResult> ExecuteReducedHht(
   status = log.Write(record); if (status.IsOk()) status = log.Flush();
   if (!status.IsOk()) return Result<DynamicExecutionResult>::Failure(status);
 
-  for (std::uint32_t increment = 1U; increment <= domain.Dynamic()->increment_count; ++increment) {
+  struct ReducedStepCandidate {
+    DynamicAcceptedFrameState frame;
+    ReducedHistory history;
+  };
+  for (std::uint32_t increment = 1U;
+       increment <= domain.Dynamic()->increment_count; ++increment) {
     const auto& old = state.CommittedState();
-    Vector pp{history.p.Size()}, vpp{history.p.Size()};
-    for (std::size_t i = 0U; i < history.p.Size(); ++i) {
-      pp[i] = history.p[i] + h * history.velocity[i] + h * h * (0.5 - parameters.beta) * history.algorithmic_acceleration[i];
-      vpp[i] = history.velocity[i] + h * (1.0 - parameters.gamma) * history.algorithmic_acceleration[i];
-    }
-    DynamicAcceptedFrameState trial_frame = old;
-    trial_frame.is_initial = false; trial_frame.frame_index = increment;
-    trial_frame.increment_index = increment; trial_frame.time = static_cast<double>(increment) * h;
-    trial_frame.time_integration_formulation = DynamicTimeIntegrationFormulation::kReducedCoordinateHht;
-    Vector trial_algorithmic{history.p.Size()};
-    Vector trial_p = pp;
-    Vector coordinate_low{history.p.Size()};
-    Vector chosen_start_p = pp;
-    Vector increment_trace{history.p.Size()};
-    Vector increment_trace_compensation{history.p.Size()};
-    Vector increment_trace_absolute_sum{history.p.Size()};
-    for (std::size_t i = 0U; i < history.p.Size(); ++i) {
-      const double velocity_term = h * history.velocity[i];
-      const double old_acceleration_term =
-          h * h * (0.5 - parameters.beta) * history.algorithmic_acceleration[i];
-      const double first_sum = history.p[i] + velocity_term;
-      coordinate_low[i] = AdditionLowPart(history.p[i], velocity_term, first_sum) +
-          AdditionLowPart(first_sum, old_acceleration_term, pp[i]);
-      AddIncrementTraceTerm(velocity_term, &increment_trace[i],
-                            &increment_trace_compensation[i]);
-      AddIncrementTraceTerm(old_acceleration_term, &increment_trace[i],
-                            &increment_trace_compensation[i]);
-      increment_trace_absolute_sum[i] =
-          std::abs(velocity_term) + std::abs(old_acceleration_term);
-    }
-    Vector seed = history.z;
-    record = {}; record.increment_index = increment; record.time = trial_frame.time; record.correction_pass = true;
-    bool translation_private_algorithmic_pass = true;
-    bool copy_translation_rates = false;
-    Vector retained_velocity{history.p.Size()};
-    Vector retained_acceleration{history.p.Size()};
-    bool accepted = false;
-    for (std::uint32_t iteration = 0U;
-         iteration <= kMaximumOuterCorrections; ++iteration) {
-      record.iteration_index = iteration; record.stage = "evaluation"; record.outcome = "candidate";
-      const auto fail = [&](const Status& failure,
-                            const char* stage = "outer") -> Result<DynamicExecutionResult> {
-        const Status contextual = WithProcedureContext(
-            domain, failure, stage, increment, trial_frame.time);
-        record.stage = stage; record.outcome = "failed";
-        record.failure_code = contextual.Diagnostics().empty()
-                                  ? "dynamic-solver-failure"
-                                  : contextual.Diagnostics().front().code;
-        const Status written = log.Write(record);
-        return Result<DynamicExecutionResult>::Failure(
-            written.IsOk() ? contextual : written);
-      };
-      Vector trial_v{history.p.Size()}, trial_a{history.p.Size()};
-      for (std::size_t i = 0U; i < trial_p.Size(); ++i) {
-        if (copy_translation_rates && PhysicalCoordinateChannel(chart.Value(), i) == 0U) {
-          trial_v[i] = retained_velocity[i];
-          trial_a[i] = retained_acceleration[i];
-        } else {
-          trial_v[i] = vpp[i] + parameters.gamma * h * trial_algorithmic[i];
-          trial_a[i] = (trial_algorithmic[i] + parameters.alpha * history.acceleration[i]) / (1.0 + parameters.alpha);
-        }
-      }
-      const auto evaluate_trial = [&](const Vector& physical_p,
-                                      const Vector& physical_v,
-                                      const Vector& physical_a,
-                                      const Vector& root_seed) -> Result<Trial> {
-        auto root = SolveEmbeddingRoot(chart.Value(), physical_p, root_seed,
-                                       [&](const Vector& q) { return position_operators(trial_frame, q); },
-                                       tangent_solver);
-        if (!root.HasValue()) return Result<Trial>::Failure(
-            WithProcedureContext(domain, root.GetStatus(), "inner-position",
-                                 increment, trial_frame.time));
-        auto rates = ReconstructPhysicalRates(chart.Value(), root.Value(), physical_v,
-                                               physical_a, tangent_solver);
-        if (!rates.HasValue()) return Result<Trial>::Failure(
-            WithProcedureContext(domain, rates.GetStatus(), "inner-rates",
-                                 increment, trial_frame.time));
-        auto candidate = trial_frame;
-        candidate.generalized_coordinates = root.Value().q;
-        candidate.velocity = rates.Value().velocity;
-        candidate.acceleration = rates.Value().acceleration;
-        candidate.algorithmic_acceleration = Vector(dofs.FullDofCount());
-        for (std::size_t i = 0U; i < candidate.algorithmic_acceleration.Size(); ++i)
-          candidate.algorithmic_acceleration[i] =
-              (1.0 + parameters.alpha) * candidate.acceleration[i] -
-              parameters.alpha * old.acceleration[i];
-        candidate.iteration_count = iteration;
-        auto assembly = EvaluateAssembly(domain, dofs, shells.Value(), candidate,
-                                         loads.Value()[1U], h, parameters,
-                                         parallel_for, true);
-        if (!assembly.HasValue()) return Result<Trial>::Failure(
-            WithProcedureContext(domain, assembly.GetStatus(), "outer",
-                                 increment, trial_frame.time));
-        assembly.Value().frame.time_integration_formulation =
-            DynamicTimeIntegrationFormulation::kReducedCoordinateHht;
-        return Result<Trial>::Success(
-            {std::move(assembly.Value()), std::move(root.Value()), physical_p,
-             physical_v, physical_a, trial_algorithmic,
-             std::move(rates.Value().z_velocity), std::move(rates.Value().z_acceleration)});
-      };
-      position_geometry_failure = false;
-      auto trial = evaluate_trial(trial_p, trial_v, trial_a, seed);
-      if (!trial.HasValue() && iteration == 0U && position_geometry_failure) {
-        for (std::size_t i = 0U; i < trial_p.Size(); ++i) {
-          trial_algorithmic[i] =
-              (history.p[i] - pp[i]) / (parameters.beta * h * h);
-          trial_p[i] = history.p[i];
-          chosen_start_p[i] = history.p[i];
-          coordinate_low[i] = 0.0;
-          increment_trace[i] = 0.0;
-          increment_trace_compensation[i] = 0.0;
-          increment_trace_absolute_sum[i] = 0.0;
-          trial_v[i] = vpp[i] + parameters.gamma * h * trial_algorithmic[i];
-          trial_a[i] = (trial_algorithmic[i] +
-                        parameters.alpha * history.acceleration[i]) /
-                       (1.0 + parameters.alpha);
-        }
-        trial = evaluate_trial(trial_p, trial_v, trial_a, seed);
-      }
-      if (!trial.HasValue()) return fail(trial.GetStatus());
-      if (iteration == 0U && !ExactlyEqual(trial_p, history.p)) {
-        Vector old_algorithmic{trial_p.Size()};
-        Vector old_velocity{trial_p.Size()};
-        Vector old_acceleration{trial_p.Size()};
-        for (std::size_t i = 0U; i < trial_p.Size(); ++i) {
-          old_algorithmic[i] = (history.p[i] - pp[i]) / (parameters.beta * h * h);
-          old_velocity[i] = vpp[i] + parameters.gamma * h * old_algorithmic[i];
-          old_acceleration[i] = (old_algorithmic[i] + parameters.alpha * history.acceleration[i]) /
-                                (1.0 + parameters.alpha);
-        }
-        auto old_trial = evaluate_trial(history.p, old_velocity, old_acceleration, seed);
-        if (!old_trial.HasValue()) return fail(old_trial.GetStatus());
-        const auto reduced_residual = [&](const Trial& value) {
-          double norm = 0.0;
-          for (const auto full : dofs.FreeDofs()) {
-            const double scale = full % 6U < 3U ? length : 1.0;
-            norm = (std::max)(norm,
-                              scale * std::abs(value.assembly.frame.residual[full]));
-          }
-          if (!std::isfinite(norm)) return std::numeric_limits<double>::infinity();
-          return norm;
-        };
-        const double old_residual = reduced_residual(old_trial.Value());
-        const double predictor_residual = reduced_residual(trial.Value());
-        if (!std::isfinite(old_residual) || !std::isfinite(predictor_residual))
-          return fail(Failure(domain, "dynamic-invalid-state",
-                              "The scaled initial reduced residual is nonfinite."));
-        if (old_residual < predictor_residual) {
-          trial = std::move(old_trial);
-          trial_p = history.p;
-          chosen_start_p = history.p;
-          coordinate_low = Vector(history.p.Size());
-          increment_trace = Vector(history.p.Size());
-          increment_trace_compensation = Vector(history.p.Size());
-          increment_trace_absolute_sum = Vector(history.p.Size());
-          trial_v = old_velocity;
-          trial_a = old_acceleration;
-          trial_algorithmic = old_algorithmic;
-        }
-      }
-      auto candidate = trial.Value().assembly.frame;
-      auto operators = EvaluateConstraintOperators(domain, dofs, shells.Value(),
-                                                   trial.Value().assembly, chart.Value(), zero, zero);
-      if (!operators.HasValue()) return fail(operators.GetStatus());
-      ResidualRecord(dofs, candidate, &record);
-      if (record.residual_pass && record.correction_pass) {
-        status = CompleteConstraintEvidence(domain, dofs, trial.Value().assembly, length, null_nodes,
-                                            positive_solver, tangent_solver, &candidate);
-        if (!status.IsOk()) return fail(status, "accepted");
-        status = CompleteEquilibrium(domain, dofs, trial.Value().assembly, &candidate);
-        if (!status.IsOk()) return fail(status, "accepted");
-        graph_regularity = CheckGraphRegularity(trial.Value().assembly,
-                                                chart.Value(), operators.Value(),
-                                                tangent_solver);
-        if (!graph_regularity.HasValue())
-          return fail(graph_regularity.GetStatus(), "accepted");
-        status = CheckReducedUpdates(domain, old, candidate, pp, vpp, trial_p, trial_v,
-                                     trial_a, trial.Value().root.z,
-                                     trial.Value().algebraic_velocity,
-                                     trial.Value().algebraic_acceleration,
-                                     trial_algorithmic, history.p, history.velocity,
-                                     history.acceleration,
-                                     history.algorithmic_acceleration,
-                                     increment_trace,
-                                     increment_trace_compensation,
-                                     increment_trace_absolute_sum,
-                                     chart.Value(), chosen_start_p, coordinate_low,
-                                     parameters, h);
-        if (!status.IsOk()) return fail(status, "accepted");
-        candidate.external_work = 0.0;
-        for (std::size_t i = 0U; i < dofs.FullDofCount(); ++i)
-          candidate.external_work += candidate.external_force[i] * candidate.generalized_coordinates[i];
-        candidate.energy_defect = candidate.kinetic_energy + candidate.physical_strain_energy +
-                                  candidate.drilling_energy - initial_energy - candidate.external_work;
-        status = state.CommitAcceptedFrame(candidate);
-        if (!status.IsOk()) return fail(status, "accepted");
-        history = {trial_p, trial_v, trial_a, trial_algorithmic, trial.Value().root.z};
-        record.stage = "accepted"; record.outcome = "accepted";
-        status = log.Write(record); if (status.IsOk()) status = log.Flush();
-        if (!status.IsOk()) return Result<DynamicExecutionResult>::Failure(status);
-        accepted = true; break;
-      }
-      if (!CanApplyOuterCorrection(iteration)) {
-        double full_hidden = 0.0;
-        double analytic_hidden = 0.0;
-        double inertia_hidden = 0.0;
-        double consistency = 0.0;
-        for (std::size_t row = 0U; row < chart.Value().null_nodes.size(); ++row) {
-          const auto node = chart.Value().null_nodes[row];
-          const auto& null = trial.Value().assembly.rotations[node].drill_null;
-          double full = 0.0;
-          double inertia = 0.0;
-          for (std::size_t component = 0U; component < 3U; ++component) {
-            const auto full_dof = 6U * node + 3U + component;
-            full += null[component] * candidate.residual[full_dof];
-            inertia += null[component] * candidate.inertia_force[full_dof];
-          }
-          const double analytic = operators.Value().rows[row].value;
-          full_hidden = (std::max)(full_hidden, std::abs(full));
-          analytic_hidden = (std::max)(analytic_hidden, std::abs(analytic));
-          inertia_hidden = (std::max)(inertia_hidden, std::abs(inertia));
-          consistency = (std::max)(consistency, std::abs(full - analytic - inertia));
-        }
-        std::ostringstream message;
-        const auto maximum = [](const Vector& values) {
-          double result = 0.0;
-          for (std::size_t i = 0U; i < values.Size(); ++i)
-            result = (std::max)(result, std::abs(values[i]));
-          return result;
-        };
-        Vector position_correction{trial_algorithmic.Size()};
-        Vector velocity_correction{trial_algorithmic.Size()};
-        for (std::size_t i = 0U; i < trial_algorithmic.Size(); ++i) {
-          position_correction[i] = parameters.beta * h * h * trial_algorithmic[i];
-          velocity_correction[i] = parameters.gamma * h * trial_algorithmic[i];
-        }
-        message << "HHT exhausted 100 corrections without satisfying every endpoint check; "
-                << "stage=outer, outer_iteration=" << iteration
-                << ", graph_iteration=" << trial.Value().root.graph_iteration_count
-                << ", graph_residual=" << trial.Value().root.graph_residual_infinity
-                << ", graph_relative=" << trial.Value().root.graph_residual_relative
-                << ", graph_correction=" << trial.Value().root.graph_correction_infinity
-                << ", max_NtE=" << full_hidden
-                << ", max_analytic_psi=" << analytic_hidden
-                << ", max_NtInertia=" << inertia_hidden
-                << ", max_NtE_minus_psi_minus_NtInertia=" << consistency
-                << ", max_pp=" << maximum(pp)
-                << ", max_beta_h2_trial_Ar=" << maximum(position_correction)
-                << ", max_trial_p=" << maximum(trial_p)
-                << ", max_vp_predictor=" << maximum(vpp)
-                << ", max_gamma_h_trial_Ar=" << maximum(velocity_correction)
-                << ", max_trial_v=" << maximum(trial_v)
-                << ", max_physical_v=" << maximum(trial.Value().velocity) << ".";
-        return fail(Failure(domain, "dynamic-nonconvergence", message.str()));
-      }
-      status = log.Write(record);
-      if (!status.IsOk()) return Result<DynamicExecutionResult>::Failure(status);
-      const double velocity_rate = parameters.gamma / (parameters.beta * h);
-      const double acceleration_rate = 1.0 / ((1.0 + parameters.alpha) * parameters.beta * h * h);
-      auto system = AssembleAugmentedReducedSystem(trial.Value().assembly, chart.Value(), operators.Value(), velocity_rate, acceleration_rate, length, h);
-      if (!system.HasValue()) return fail(system.GetStatus());
-      const bool angular_only = ShouldRefineAngular(
-          chart.Value(), candidate.free_residual_metrics,
-          {record.coordinate_correction[0U], record.velocity_correction[0U],
-           record.acceleration_correction[0U], record.algorithmic_correction[0U]},
-          translation_private_algorithmic_pass);
-      auto selected = SelectAugmentedSolve(system.Value(), chart.Value(), angular_only);
-      if (!selected.HasValue()) return fail(selected.GetStatus());
-      const auto linear_failure = [&](const Status& failure) {
-        return fail(failure, angular_only ? "angular-newton-linear-solve"
-                                         : "full-newton-linear-solve");
-      };
-      Vector selected_solution{selected.Value().rhs.Size()};
-      if (selected_solution.Size() > 0U) {
-        status = tangent_solver.FactorizeFresh(selected.Value().tangent);
-        if (!status.IsOk()) return linear_failure(status);
-        status = tangent_solver.SolveCorrection(selected.Value().rhs, selected_solution);
-        if (!status.IsOk()) return linear_failure(status);
-        status = CheckLinearSolve(selected.Value().tangent, selected.Value().rhs, selected_solution);
-        if (!status.IsOk()) return linear_failure(status);
-      }
-      auto solution = EmbedAugmentedSolution(selected.Value(), selected_solution,
-                                             system.Value().rhs.Size());
-      if (!solution.HasValue()) return fail(solution.GetStatus());
-      auto correction = MapAugmentedCorrection(chart.Value(), system.Value(), solution.Value(), velocity_rate, acceleration_rate);
-      if (!correction.HasValue()) return fail(correction.GetStatus());
-      Vector full_algorithmic{dofs.FullDofCount()};
-      Vector reduced_algorithmic{correction.Value().p.Size()};
-      Vector reduced_physical{correction.Value().p.Size()};
-      for (std::size_t i = 0U; i < full_algorithmic.Size(); ++i)
-        full_algorithmic[i] =
-            (1.0 + parameters.alpha) * correction.Value().acceleration[i];
-      for (std::size_t i = 0U; i < reduced_algorithmic.Size(); ++i) {
-        reduced_algorithmic[i] = correction.Value().p[i] /
-                                 (parameters.beta * h * h);
-        reduced_physical[i] = acceleration_rate * correction.Value().p[i];
-      }
-      CorrectionRecord(correction.Value().coordinate, correction.Value().velocity,
-                       correction.Value().acceleration, full_algorithmic,
-                       reduced_algorithmic, reduced_physical, chart.Value(), dofs, length, h,
-                       parameters.alpha,
-                       &record);
-      translation_private_algorithmic_pass = true;
-      for (std::size_t i = 0U; i < chart.Value().p_dofs.size(); ++i)
-        if (PhysicalCoordinateChannel(chart.Value(), i) == 0U)
-          translation_private_algorithmic_pass =
-              translation_private_algorithmic_pass &&
-              PrivateCorrectionEqual(chart.Value(), i, full_algorithmic,
-                                     reduced_algorithmic, reduced_physical, parameters.alpha);
-      copy_translation_rates = angular_only;
-      if (angular_only) {
-        retained_velocity = trial_v;
-        retained_acceleration = trial_a;
-      }
-      for (std::size_t i = 0U; i < trial_algorithmic.Size(); ++i) {
-        if (angular_only && PhysicalCoordinateChannel(chart.Value(), i) == 0U) continue;
-        trial_algorithmic[i] += reduced_algorithmic[i];
-      }
-      for (std::size_t i = 0U; i < trial_p.Size(); ++i) {
-        if (angular_only && PhysicalCoordinateChannel(chart.Value(), i) == 0U) continue;
-        AdvanceCoordinate(correction.Value().p[i], &trial_p[i], &coordinate_low[i]);
-      }
-      for (std::size_t i = 0U; i < increment_trace.Size(); ++i) {
-        if (angular_only && PhysicalCoordinateChannel(chart.Value(), i) == 0U) continue;
-        AddIncrementTraceTerm(correction.Value().p[i], &increment_trace[i],
-                              &increment_trace_compensation[i]);
-        increment_trace_absolute_sum[i] += std::abs(correction.Value().p[i]);
-      }
-      seed = trial.Value().root.z;
-      for (std::size_t i = 0U; i < seed.Size(); ++i)
-        seed[i] += correction.Value().z[i];
-    }
-    if (!accepted) return Result<DynamicExecutionResult>::Failure(
-        Failure(domain, "dynamic-nonconvergence", "Dynamic increment was not accepted."));
+    const auto report_failure = [&](const Status& failure, const char* stage) {
+      const Status contextual = WithProcedureContext(
+          domain, failure, stage, increment, record.time);
+      record.stage = stage;
+      record.outcome = "failed";
+      record.failure_code = contextual.Diagnostics().empty()
+                                ? "dynamic-solver-failure"
+                                : contextual.Diagnostics().front().code;
+      const Status written = log.Write(record);
+      return written.IsOk() ? contextual : written;
+    };
+    status = RunReducedHhtStep(
+        integrator, history, h, parameters,
+        [&](const ShellHhtIntegrator& step_integrator,
+            ReducedShellPredictor predictor) -> Result<ReducedStepCandidate> {
+          Vector pp = std::move(predictor.pp);
+          Vector vpp = std::move(predictor.vpp);
+          DynamicAcceptedFrameState trial_frame = old;
+          trial_frame.is_initial = false;
+          trial_frame.frame_index = increment;
+          trial_frame.increment_index = increment;
+          trial_frame.time = static_cast<double>(increment) * h;
+          trial_frame.time_integration_formulation =
+              DynamicTimeIntegrationFormulation::kReducedCoordinateHht;
+          Vector trial_algorithmic{history.p.Size()};
+          Vector trial_p = pp;
+          Vector coordinate_low = std::move(predictor.coordinate_low);
+          Vector chosen_start_p = pp;
+          Vector increment_trace = std::move(predictor.increment_trace);
+          Vector increment_trace_compensation =
+              std::move(predictor.increment_trace_compensation);
+          Vector increment_trace_absolute_sum =
+              std::move(predictor.increment_trace_absolute_sum);
+          Vector seed = history.z;
+          record = {};
+          record.increment_index = increment;
+          record.time = trial_frame.time;
+          record.correction_pass = true;
+          bool translation_private_algorithmic_pass = true;
+          bool copy_translation_rates = false;
+          Vector retained_velocity{history.p.Size()};
+          Vector retained_acceleration{history.p.Size()};
+          using StepResult = Result<std::optional<ReducedStepCandidate>>;
+          const auto write_iteration =
+              [&](const DynamicNewtonIterationLogRecord& value) {
+                return log.Write(value);
+              };
+          ReducedShellHhtStep<ReducedStepCandidate> iteration_step(
+              [&](std::uint32_t iteration) -> StepResult {
+                record.iteration_index = iteration;
+                record.stage = "evaluation";
+                record.outcome = "candidate";
+                const auto fail = [&](const Status& failure,
+                                      const char* stage = "outer") -> StepResult {
+                  return StepResult::Failure(report_failure(failure, stage));
+                };
+                ReducedShellTrialRates reduced_rates{
+                    Vector{history.p.Size()}, Vector{history.p.Size()}};
+                step_integrator.EvaluateRates(
+                    {chart.Value(), history, trial_algorithmic, vpp,
+                     copy_translation_rates, retained_velocity, retained_acceleration,
+                     h, parameters}, reduced_rates.velocity,
+                    reduced_rates.acceleration);
+                Vector trial_v = std::move(reduced_rates.velocity);
+                Vector trial_a = std::move(reduced_rates.acceleration);
+                const auto evaluate_trial =
+                    [&](const Vector& physical_p, const Vector& physical_v,
+                        const Vector& physical_a,
+                        const Vector& root_seed) -> Result<Trial> {
+                  auto root = SolveEmbeddingRoot(
+                      chart.Value(), physical_p, root_seed,
+                      [&](const Vector& q) {
+                        return position_operators(trial_frame, q);
+                      },
+                      tangent_solver);
+                  if (!root.HasValue())
+                    return Result<Trial>::Failure(WithProcedureContext(
+                        domain, root.GetStatus(), "inner-position", increment,
+                        trial_frame.time));
+                  auto rates = step_integrator.ReconstructPhysicalRates(
+                      chart.Value(), root.Value(), physical_v, physical_a,
+                      tangent_solver);
+                  if (!rates.HasValue())
+                    return Result<Trial>::Failure(
+                        WithProcedureContext(domain, rates.GetStatus(), "inner-rates",
+                                             increment, trial_frame.time));
+                  auto candidate = trial_frame;
+                  candidate.generalized_coordinates = root.Value().q;
+                  candidate.velocity = rates.Value().velocity;
+                  candidate.acceleration = rates.Value().acceleration;
+                  candidate.algorithmic_acceleration = Vector(dofs.FullDofCount());
+                  for (std::size_t i = 0U;
+                       i < candidate.algorithmic_acceleration.Size(); ++i)
+                    candidate.algorithmic_acceleration[i] =
+                        (1.0 + parameters.alpha) * candidate.acceleration[i] -
+                        parameters.alpha * old.acceleration[i];
+                  candidate.iteration_count = iteration;
+                  auto assembly = EvaluateAssembly(domain, dofs, shells.Value(),
+                                                   candidate, loads.Value()[1U], h,
+                                                   parameters, parallel_for, true);
+                  if (!assembly.HasValue())
+                    return Result<Trial>::Failure(
+                        WithProcedureContext(domain, assembly.GetStatus(), "outer",
+                                             increment, trial_frame.time));
+                  assembly.Value().frame.time_integration_formulation =
+                      DynamicTimeIntegrationFormulation::kReducedCoordinateHht;
+                  return Result<Trial>::Success(
+                      {std::move(assembly.Value()), std::move(root.Value()),
+                       physical_p, physical_v, physical_a, trial_algorithmic,
+                       std::move(rates.Value().z_velocity),
+                       std::move(rates.Value().z_acceleration)});
+                };
+                position_geometry_failure = false;
+                auto trial = evaluate_trial(trial_p, trial_v, trial_a, seed);
+                if (!trial.HasValue() && iteration == 0U &&
+                    position_geometry_failure) {
+                  for (std::size_t i = 0U; i < trial_p.Size(); ++i) {
+                    trial_algorithmic[i] =
+                        (history.p[i] - pp[i]) / (parameters.beta * h * h);
+                    trial_p[i] = history.p[i];
+                    chosen_start_p[i] = history.p[i];
+                    coordinate_low[i] = 0.0;
+                    increment_trace[i] = 0.0;
+                    increment_trace_compensation[i] = 0.0;
+                    increment_trace_absolute_sum[i] = 0.0;
+                  }
+                  step_integrator.EvaluateRates(
+                      {chart.Value(), history, trial_algorithmic, vpp, false,
+                       retained_velocity, retained_acceleration, h, parameters},
+                      trial_v, trial_a);
+                  trial = evaluate_trial(trial_p, trial_v, trial_a, seed);
+                }
+                if (!trial.HasValue())
+                  return fail(trial.GetStatus());
+                if (iteration == 0U && !ExactlyEqual(trial_p, history.p)) {
+                  Vector old_algorithmic{trial_p.Size()};
+                  Vector old_velocity{trial_p.Size()};
+                  Vector old_acceleration{trial_p.Size()};
+                  for (std::size_t i = 0U; i < trial_p.Size(); ++i) {
+                    old_algorithmic[i] =
+                        (history.p[i] - pp[i]) / (parameters.beta * h * h);
+                  }
+                  step_integrator.EvaluateRates(
+                      {chart.Value(), history, old_algorithmic, vpp, false,
+                       retained_velocity, retained_acceleration, h, parameters},
+                      old_velocity, old_acceleration);
+                  auto old_trial =
+                      evaluate_trial(history.p, old_velocity, old_acceleration, seed);
+                  if (!old_trial.HasValue())
+                    return fail(old_trial.GetStatus());
+                  const auto reduced_residual = [&](const Trial& value) {
+                    double norm = 0.0;
+                    for (const auto full : dofs.FreeDofs()) {
+                      const double scale = full % 6U < 3U ? length : 1.0;
+                      norm = (std::max)(norm,
+                                        scale *
+                                            std::abs(
+                                                value.assembly.frame.residual[full]));
+                    }
+                    if (!std::isfinite(norm))
+                      return std::numeric_limits<double>::infinity();
+                    return norm;
+                  };
+                  const double old_residual = reduced_residual(old_trial.Value());
+                  const double predictor_residual = reduced_residual(trial.Value());
+                  if (!std::isfinite(old_residual) ||
+                      !std::isfinite(predictor_residual))
+                    return fail(
+                        Failure(domain, "dynamic-invalid-state",
+                                "The scaled initial reduced residual is nonfinite."));
+                  if (old_residual < predictor_residual) {
+                    trial = std::move(old_trial);
+                    trial_p = history.p;
+                    chosen_start_p = history.p;
+                    coordinate_low = Vector(history.p.Size());
+                    increment_trace = Vector(history.p.Size());
+                    increment_trace_compensation = Vector(history.p.Size());
+                    increment_trace_absolute_sum = Vector(history.p.Size());
+                    trial_v = old_velocity;
+                    trial_a = old_acceleration;
+                    trial_algorithmic = old_algorithmic;
+                  }
+                }
+                auto candidate = trial.Value().assembly.frame;
+                auto operators = EvaluateConstraintOperators(
+                    domain, dofs, shells.Value(), trial.Value().assembly,
+                    chart.Value(), zero, zero);
+                if (!operators.HasValue())
+                  return fail(operators.GetStatus());
+                ResidualRecord(dofs, candidate, &record);
+                if (record.residual_pass && record.correction_pass) {
+                  status = CompleteConstraintEvidence(
+                      domain, dofs, trial.Value().assembly, length, null_nodes,
+                      positive_solver, tangent_solver, &candidate);
+                  if (!status.IsOk())
+                    return fail(status, "accepted");
+                  status = CompleteEquilibrium(domain, dofs, trial.Value().assembly,
+                                               &candidate);
+                  if (!status.IsOk())
+                    return fail(status, "accepted");
+                  graph_regularity =
+                      CheckGraphRegularity(trial.Value().assembly, chart.Value(),
+                                           operators.Value(), tangent_solver);
+                  if (!graph_regularity.HasValue())
+                    return fail(graph_regularity.GetStatus(), "accepted");
+                  status = CheckReducedUpdates(
+                      domain, old, candidate, pp, vpp, trial_p, trial_v, trial_a,
+                      trial.Value().root.z, trial.Value().algebraic_velocity,
+                      trial.Value().algebraic_acceleration, trial_algorithmic,
+                      history.p, history.velocity, history.acceleration,
+                      history.algorithmic_acceleration, increment_trace,
+                      increment_trace_compensation, increment_trace_absolute_sum,
+                      chart.Value(), chosen_start_p, coordinate_low, parameters, h);
+                  if (!status.IsOk())
+                    return fail(status, "accepted");
+                  candidate.external_work = 0.0;
+                  for (std::size_t i = 0U; i < dofs.FullDofCount(); ++i)
+                    candidate.external_work += candidate.external_force[i] *
+                                               candidate.generalized_coordinates[i];
+                  candidate.energy_defect = candidate.kinetic_energy +
+                                            candidate.physical_strain_energy +
+                                            candidate.drilling_energy -
+                                            initial_energy - candidate.external_work;
+                  return StepResult::Success(ReducedStepCandidate{
+                      std::move(candidate),
+                      {trial_p, trial_v, trial_a, trial_algorithmic,
+                       trial.Value().root.z}});
+                }
+                if (!CanApplyOuterCorrection(iteration)) {
+                  double full_hidden = 0.0;
+                  double analytic_hidden = 0.0;
+                  double inertia_hidden = 0.0;
+                  double consistency = 0.0;
+                  for (std::size_t row = 0U; row < chart.Value().null_nodes.size();
+                       ++row) {
+                    const auto node = chart.Value().null_nodes[row];
+                    const auto& null =
+                        trial.Value().assembly.rotations[node].drill_null;
+                    double full = 0.0;
+                    double inertia = 0.0;
+                    for (std::size_t component = 0U; component < 3U; ++component) {
+                      const auto full_dof = 6U * node + 3U + component;
+                      full += null[component] * candidate.residual[full_dof];
+                      inertia += null[component] * candidate.inertia_force[full_dof];
+                    }
+                    const double analytic = operators.Value().rows[row].value;
+                    full_hidden = (std::max)(full_hidden, std::abs(full));
+                    analytic_hidden = (std::max)(analytic_hidden, std::abs(analytic));
+                    inertia_hidden = (std::max)(inertia_hidden, std::abs(inertia));
+                    consistency =
+                        (std::max)(consistency, std::abs(full - analytic - inertia));
+                  }
+                  std::ostringstream message;
+                  const auto maximum = [](const Vector& values) {
+                    double result = 0.0;
+                    for (std::size_t i = 0U; i < values.Size(); ++i)
+                      result = (std::max)(result, std::abs(values[i]));
+                    return result;
+                  };
+                  Vector position_correction{trial_algorithmic.Size()};
+                  Vector velocity_correction{trial_algorithmic.Size()};
+                  for (std::size_t i = 0U; i < trial_algorithmic.Size(); ++i) {
+                    position_correction[i] =
+                        parameters.beta * h * h * trial_algorithmic[i];
+                    velocity_correction[i] =
+                        parameters.gamma * h * trial_algorithmic[i];
+                  }
+                  message << "HHT exhausted 100 corrections without satisfying every "
+                             "endpoint check; "
+                          << "stage=outer, outer_iteration=" << iteration
+                          << ", graph_iteration="
+                          << trial.Value().root.graph_iteration_count
+                          << ", graph_residual="
+                          << trial.Value().root.graph_residual_infinity
+                          << ", graph_relative="
+                          << trial.Value().root.graph_residual_relative
+                          << ", graph_correction="
+                          << trial.Value().root.graph_correction_infinity
+                          << ", max_NtE=" << full_hidden
+                          << ", max_analytic_psi=" << analytic_hidden
+                          << ", max_NtInertia=" << inertia_hidden
+                          << ", max_NtE_minus_psi_minus_NtInertia=" << consistency
+                          << ", max_pp=" << maximum(pp)
+                          << ", max_beta_h2_trial_Ar=" << maximum(position_correction)
+                          << ", max_trial_p=" << maximum(trial_p)
+                          << ", max_vp_predictor=" << maximum(vpp)
+                          << ", max_gamma_h_trial_Ar=" << maximum(velocity_correction)
+                          << ", max_trial_v=" << maximum(trial_v)
+                          << ", max_physical_v=" << maximum(trial.Value().velocity)
+                          << ".";
+                  return fail(
+                      Failure(domain, "dynamic-nonconvergence", message.str()));
+                }
+                status = write_iteration(record);
+                if (!status.IsOk())
+                  return StepResult::Failure(status);
+                const double velocity_rate = parameters.gamma / (parameters.beta * h);
+                const double acceleration_rate =
+                    1.0 / ((1.0 + parameters.alpha) * parameters.beta * h * h);
+                auto system = AssembleAugmentedReducedSystem(
+                    trial.Value().assembly, chart.Value(), operators.Value(),
+                    velocity_rate, acceleration_rate, length, h);
+                if (!system.HasValue())
+                  return fail(system.GetStatus());
+                const bool angular_only = ShouldRefineAngular(
+                    chart.Value(), candidate.free_residual_metrics,
+                    {record.coordinate_correction[0U], record.velocity_correction[0U],
+                     record.acceleration_correction[0U],
+                     record.algorithmic_correction[0U]},
+                    translation_private_algorithmic_pass);
+                auto selected =
+                    SelectAugmentedSolve(system.Value(), chart.Value(), angular_only);
+                if (!selected.HasValue())
+                  return fail(selected.GetStatus());
+                const auto linear_failure = [&](const Status& failure) {
+                  return fail(failure, angular_only ? "angular-newton-linear-solve"
+                                                    : "full-newton-linear-solve");
+                };
+                Vector selected_solution{selected.Value().rhs.Size()};
+                if (selected_solution.Size() > 0U) {
+                  status = tangent_solver.FactorizeFresh(selected.Value().tangent);
+                  if (!status.IsOk())
+                    return linear_failure(status);
+                  status = tangent_solver.SolveCorrection(selected.Value().rhs,
+                                                          selected_solution);
+                  if (!status.IsOk())
+                    return linear_failure(status);
+                  status = CheckLinearSolve(selected.Value().tangent,
+                                            selected.Value().rhs, selected_solution);
+                  if (!status.IsOk())
+                    return linear_failure(status);
+                }
+                auto solution = EmbedAugmentedSolution(
+                    selected.Value(), selected_solution, system.Value().rhs.Size());
+                if (!solution.HasValue())
+                  return fail(solution.GetStatus());
+                auto correction = MapAugmentedCorrection(
+                    chart.Value(), system.Value(), solution.Value(), velocity_rate,
+                    acceleration_rate);
+                if (!correction.HasValue())
+                  return fail(correction.GetStatus());
+                Vector full_algorithmic{dofs.FullDofCount()};
+                Vector reduced_algorithmic{correction.Value().p.Size()};
+                Vector reduced_physical{correction.Value().p.Size()};
+                for (std::size_t i = 0U; i < full_algorithmic.Size(); ++i)
+                  full_algorithmic[i] =
+                      (1.0 + parameters.alpha) * correction.Value().acceleration[i];
+                for (std::size_t i = 0U; i < reduced_algorithmic.Size(); ++i) {
+                  reduced_algorithmic[i] =
+                      correction.Value().p[i] / (parameters.beta * h * h);
+                  reduced_physical[i] = acceleration_rate * correction.Value().p[i];
+                }
+                CorrectionRecord(correction.Value().coordinate,
+                                 correction.Value().velocity,
+                                 correction.Value().acceleration, full_algorithmic,
+                                 reduced_algorithmic, reduced_physical, chart.Value(),
+                                 dofs, length, h, parameters.alpha, &record);
+                translation_private_algorithmic_pass = true;
+                for (std::size_t i = 0U; i < chart.Value().p_dofs.size(); ++i)
+                  if (PhysicalCoordinateChannel(chart.Value(), i) == 0U)
+                    translation_private_algorithmic_pass =
+                        translation_private_algorithmic_pass &&
+                        PrivateCorrectionEqual(chart.Value(), i, full_algorithmic,
+                                               reduced_algorithmic, reduced_physical,
+                                               parameters.alpha);
+                copy_translation_rates = angular_only;
+                if (angular_only) {
+                  retained_velocity = trial_v;
+                  retained_acceleration = trial_a;
+                }
+                for (std::size_t i = 0U; i < trial_algorithmic.Size(); ++i) {
+                  if (angular_only &&
+                      PhysicalCoordinateChannel(chart.Value(), i) == 0U)
+                    continue;
+                  trial_algorithmic[i] += reduced_algorithmic[i];
+                }
+                for (std::size_t i = 0U; i < trial_p.Size(); ++i) {
+                  if (angular_only &&
+                      PhysicalCoordinateChannel(chart.Value(), i) == 0U)
+                    continue;
+                  AdvanceCoordinate(correction.Value().p[i], &trial_p[i],
+                                    &coordinate_low[i]);
+                }
+                for (std::size_t i = 0U; i < increment_trace.Size(); ++i) {
+                  if (angular_only &&
+                      PhysicalCoordinateChannel(chart.Value(), i) == 0U)
+                    continue;
+                  AddIncrementTraceTerm(correction.Value().p[i], &increment_trace[i],
+                                        &increment_trace_compensation[i]);
+                  increment_trace_absolute_sum[i] +=
+                      std::abs(correction.Value().p[i]);
+                }
+                seed = trial.Value().root.z;
+                for (std::size_t i = 0U; i < seed.Size(); ++i)
+                  seed[i] += correction.Value().z[i];
+                return StepResult::Success(std::nullopt);
+              },
+              kMaximumOuterCorrections);
+          const Status solved = iteration_step.Solve(algorithm);
+          if (!solved.IsOk())
+            return Result<ReducedStepCandidate>::Failure(solved);
+          if (!iteration_step.HasCandidate()) return Result<ReducedStepCandidate>::Failure(
+              Failure(domain, "dynamic-nonconvergence", "Dynamic increment was not accepted."));
+          return Result<ReducedStepCandidate>::Success(
+              iteration_step.TakeCandidate());
+        },
+        [&](ReducedStepCandidate&& accepted_candidate) -> Status {
+          status = state.CommitAcceptedFrame(accepted_candidate.frame);
+          if (!status.IsOk())
+            return report_failure(status, "accepted");
+          history = std::move(accepted_candidate.history);
+          record.stage = "accepted";
+          record.outcome = "accepted";
+          status = log.Write(record);
+          if (status.IsOk())
+            status = log.Flush();
+          return status;
+        });
+    if (!status.IsOk()) return Result<DynamicExecutionResult>::Failure(status);
   }
-  return Result<DynamicExecutionResult>::Success({std::move(state), domain.Warnings()});
+  return Result<DynamicExecutionResult>::Success(
+      {std::move(state), domain.Warnings()});
 }
-}  // namespace fesa
+} // namespace fesa

src/fesa/analysis/hht_reduced_procedure.h

@@ -3,16 +3,20 @@
 
 #include <cstdint>
 
-#include "fesa/analysis/prepared_analysis.h"
+#include "fesa/analysis/dynamic_execution_result.h"
+#include "fesa/core/status.h"
 
 namespace fesa {
 namespace hht_reduced_internal {
+class ShellHhtIntegrator;
 constexpr std::uint32_t kMaximumOuterCorrections = 100U;
 constexpr bool CanApplyOuterCorrection(const std::uint32_t completed) {
   return completed < kMaximumOuterCorrections;
 }
 }  // namespace hht_reduced_internal
 
+class Domain;
+class EquilibriumAlgorithm;
 class LinearSolver;
 class NewtonIterationLogWriter;
 class ParallelFor;
@@ -22,6 +26,14 @@ Result<DynamicExecutionResult> ExecuteReducedHht(
     const Domain& domain, NewtonIterationLogWriter& log,
     const ParallelFor& parallel_for, LinearSolver& positive_solver,
     TangentSolver& tangent_solver);
+
+/// @brief Borrows caller iteration policy for the complete production core.
+Result<DynamicExecutionResult> ExecuteReducedHht(
+    const Domain& domain, NewtonIterationLogWriter& log,
+    const ParallelFor& parallel_for, LinearSolver& positive_solver,
+    TangentSolver& tangent_solver,
+    const hht_reduced_internal::ShellHhtIntegrator& integrator,
+    EquilibriumAlgorithm& algorithm);
 }  // namespace fesa
 
 #endif  // FESA_ANALYSIS_HHT_REDUCED_PROCEDURE_H_

src/fesa/analysis/linear_frequency_procedure.cpp

@@ -20,6 +20,7 @@
 #include "fesa/elements/mitc4_shell.h"
 #include "fesa/fem/dof_manager.h"
 #include "fesa/math/sparse_matrix.h"
+#include "fesa/solvers/eigen/mkl_feast_eigen_solver.h"
 
 namespace fesa {
 namespace {
@@ -84,7 +85,8 @@ double MaximumEdgeLength(const Domain& domain) {
   return maximum;
 }
 
-Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain) {
+Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain,
+                                          const EigenSolver& solver) {
   const FrequencyStepDefinition* frequency = domain.Frequency();
   if (frequency == nullptr || domain.Steps().Size() != 1U) {
     return Result<EigenAnalysisState>::Failure(
@@ -101,6 +103,7 @@ Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain) {
     return Result<EigenAnalysisState>::Failure(model.GetStatus());
   const ElementFactory factory;
   std::vector<std::unique_ptr<Element>> owned;
+  std::vector<std::unique_ptr<ShellReferenceElement>> references;
   ElementView view;
   owned.reserve(model.Value().ActiveElements().size());
   view.reserve(model.Value().ActiveElements().size());
@@ -108,13 +111,15 @@ Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain) {
     auto element = factory.Create(domain.Elements()[index], domain);
     if (!element.HasValue())
       return Result<EigenAnalysisState>::Failure(element.GetStatus());
-    if (dynamic_cast<const Mitc4Shell*>(element.Value().get()) == nullptr) {
+    auto reference = factory.BindShellReference(*element.Value());
+    if (reference == nullptr) {
       return Result<EigenAnalysisState>::Failure(Failure(
           "unsupported-frequency-element", std::to_string(index),
           "The frequency procedure supports MITC4 shell elements only."));
     }
     view.emplace_back(*element.Value());
     owned.push_back(std::move(element.Value()));
+    references.push_back(std::move(reference));
   }
   DofManager dofs;
   const Status dof_status = dofs.Build(model.Value(), view);
@@ -158,7 +163,7 @@ Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain) {
                   std::to_string(definition.MaterialIndex()),
                   "Every active shell material requires a positive density."));
     }
-    const auto* element = dynamic_cast<const Mitc4Shell*>(owned[shell].get());
+    const auto& element = references[shell];
     auto mass = element->Mass(density[definition.MaterialIndex()]);
     auto shell_stiffness = element->Stiffness();
     if (!mass.HasValue())
@@ -207,7 +212,7 @@ Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain) {
                             (material->YoungsModulus() / density[material_id]) /
                                 length / length);
   }
-  auto backend = MklFeastEigenSolver{}.Solve(
+  auto backend = solver.Solve(
       reduction.Value().whitened_operator, request, zero_scale);
   if (!backend.HasValue())
     return Result<EigenAnalysisState>::Failure(backend.GetStatus());
@@ -403,7 +408,8 @@ Result<EigenAnalysisState> ExecuteCandidate(const Domain& domain) {
 Result<EigenAnalysisState> LinearFrequencyProcedureExecutor::Execute(
     const Domain& domain) const {
   try {
-    auto result = ExecuteCandidate(domain);
+    const MklFeastEigenSolver default_solver;
+    auto result = ExecuteCandidate(domain, solver_ ? *solver_ : default_solver);
     if (!result.HasValue()) {
       auto diagnostics = result.GetStatus().Diagnostics();
       for (auto& diagnostic : diagnostics) {

src/fesa/analysis/linear_static_procedure.cpp

@@ -142,7 +142,7 @@ Result<LinearStaticExecutionResult> LinearStaticProcedureExecutor::Execute(
   }
   state.ExternalForce() = std::move(nodal_external.Value());
 
-  Result<Vector> rhs = LoadAssembler::EffectiveFreeRhs(
+  Result<Vector> rhs = EssentialConstraintPolicy{}.EffectiveFreeRhs(
       state.ExternalForce(), partitions.Value().k_fc, dofs.PrescribedValues(),
       dofs);
   if (!rhs.HasValue()) {

src/fesa/analysis/nonlinear_analysis_state.cpp

@@ -1,6 +1,5 @@
 #include "fesa/analysis/nonlinear_analysis_state.h"
 
-#include <algorithm>
 #include <array>
 #include <cmath>
 #include <cstddef>
@@ -9,11 +8,18 @@
 #include <utility>
 #include <vector>
 
+#include "fesa/core/source_identity.h"
 #include "fesa/elements/element_definition.h"
+#include "math/finite_values.h"
+#include "results/shell_result_recovery.h"
+#include "analysis/shell_state_inventory.h"
 
 namespace fesa {
 namespace {
 
+using analysis_internal::ShellElementOrder;
+using math_internal::IsFinite;
+
 constexpr std::size_t kDofsPerNode = 6U;
 constexpr std::size_t kShellLocationsPerElement = 4U;
 constexpr std::uint32_t kMaximumNewtonIterations = 100U;
@@ -27,59 +33,6 @@ Status StateFailure(const FailureCategory category, const std::string& code,
         message}});
 }
 
-/// @brief Compares every preserved source-identity component.
-bool SourceIdsMatch(const SourceEntityId& left, const SourceEntityId& right) {
-  return left.instance_name == right.instance_name &&
-         left.source_label == right.source_label &&
-         left.source_label_text == right.source_label_text;
-}
-
-template <std::size_t Size>
-/// @brief Tests one fixed-size numerical array for finite values.
-bool IsFinite(const std::array<double, Size>& values) {
-  return std::all_of(values.begin(), values.end(),
-                     [](const double value) { return std::isfinite(value); });
-}
-
-/// @brief Tests each component of a stored trial vector for finiteness.
-bool IsFinite(const Vector& values) {
-  for (std::size_t index = 0U; index < values.Size(); ++index) {
-    if (!std::isfinite(values[index])) {
-      return false;
-    }
-  }
-  return true;
-}
-
-/// @brief Tests all physical quantities attached to one shell recovery row.
-bool IsFinite(const ShellResultRow& row) {
-  if (!IsFinite(row.natural_coordinates) || !IsFinite(row.generalized_strain) ||
-      !IsFinite(row.section_resultant)) {
-    return false;
-  }
-  for (const auto& axis : row.local_frame) {
-    if (!IsFinite(axis)) {
-      return false;
-    }
-  }
-  return std::all_of(row.stress.begin(), row.stress.end(),
-                     [](const ShellSectionStressRow& stress) {
-                       return std::isfinite(stress.zeta) &&
-                              IsFinite(stress.components);
-                     });
-}
-
-/// @brief Returns shell Domain indices in deterministic unified element order.
-std::vector<EntityIndex> ShellElementOrder(const Domain& domain) {
-  std::vector<EntityIndex> order;
-  for (std::size_t index = 0U; index < domain.Elements().Size(); ++index) {
-    if (domain.Elements()[index].Kind() == ElementDefinitionKind::kMitc4Shell) {
-      order.push_back(static_cast<EntityIndex>(index));
-    }
-  }
-  return order;
-}
-
 /// @brief Validates one accepted frame before any committed-state mutation.
 Status ValidateAcceptedFrame(const AcceptedFrameState& frame,
                              const NonlinearTrialState& committed,
@@ -117,7 +70,7 @@ Status ValidateAcceptedFrame(const AcceptedFrameState& frame,
   for (std::size_t node = 0U; node < node_count; ++node) {
     if (frame.nodal_internal_order[node] !=
             committed.nodal_internal_order[node] ||
-        !SourceIdsMatch(frame.nodal_source_ids[node],
+        !SourceIdentityEquals(frame.nodal_source_ids[node],
                          committed.nodal_source_ids[node]) ||
         !IsFinite(frame.nodal_triad[node][0U]) ||
         !IsFinite(frame.nodal_triad[node][1U]) ||
@@ -179,7 +132,7 @@ Status ValidateAcceptedFrame(const AcceptedFrameState& frame,
       if (row.element != shell_order[element] ||
           row.location != expected_locations[point] ||
           row.natural_coordinates != expected_coordinates[point] ||
-          !IsFinite(row)) {
+          !results_internal::IsFiniteShellRow(row)) {
         return StateFailure(FailureCategory::kSolver, "invalid-accepted-state", {},
                             "Shell result rows do not preserve stable identity.");
       }
@@ -241,7 +194,7 @@ Result<NonlinearAnalysisState> NonlinearAnalysisState::Create(
   for (std::size_t node = 0U; node < node_count; ++node) {
     const auto& entry = baseline.node_baselines[node];
     if (entry.node_index != static_cast<EntityIndex>(node) ||
-        !SourceIdsMatch(entry.source_id, domain.Nodes()[node].source_id) ||
+        !SourceIdentityEquals(entry.source_id, domain.Nodes()[node].source_id) ||
         !IsFinite(entry.triad[0U]) || !IsFinite(entry.triad[1U]) ||
         !IsFinite(entry.triad[2U]) || !IsFinite(entry.director)) {
       return Result<NonlinearAnalysisState>::Failure(StateFailure(

src/fesa/analysis/nonlinear_static_control.cpp

@@ -12,10 +12,17 @@
 #include "fesa/analysis/analysis_model.h"
 #include "fesa/assembly/load_assembler.h"
 #include "fesa/elements/finite_rotation.h"
+#include "math/vector3_operations.h"
+#include "elements/shell_kernel_values.h"
+#include "math/dense_blas_internal.h"
 
 namespace fesa {
 namespace {
 
+using shell_kernel_internal::FrameMatrix;
+using math_internal::Multiply;
+using math_internal::Skew;
+
 constexpr std::size_t kDofsPerNode = 6U;
 constexpr std::size_t kTranslationDofCount = 3U;
 constexpr double kMomentAdmissibilityThreshold = 1.0e-12;
@@ -67,27 +74,6 @@ Result<Vector3> RotationVectorForNode(const Vector& trial,
   return Result<Vector3>::Success(rotation);
 }
 
-/// @brief Builds a proper initial frame from its semantic nodal record.
-Matrix InitialFrame(const ShellNodeInitialFrame& frame) {
-  Matrix result{3U, 3U};
-  for (std::size_t row = 0U; row < kTranslationDofCount; ++row) {
-    result(row, 0U) = frame.tangent_a[row];
-    result(row, 1U) = frame.tangent_b[row];
-    result(row, 2U) = frame.director[row];
-  }
-  return result;
-}
-
-/// @brief Multiplies a 3-by-3 matrix by a Vector3.
-Vector3 Multiply(const Matrix& matrix, const Vector3& vector) {
-  return {matrix(0U, 0U) * vector.X() + matrix(0U, 1U) * vector.Y() +
-              matrix(0U, 2U) * vector.Z(),
-          matrix(1U, 0U) * vector.X() + matrix(1U, 1U) * vector.Y() +
-              matrix(1U, 2U) * vector.Z(),
-          matrix(2U, 0U) * vector.X() + matrix(2U, 1U) * vector.Y() +
-              matrix(2U, 2U) * vector.Z()};
-}
-
 /// @brief Multiplies a 3-by-3 matrix transpose by a Vector3.
 Vector3 MultiplyTranspose(const Matrix& matrix, const Vector3& vector) {
   return {matrix(0U, 0U) * vector.X() + matrix(1U, 0U) * vector.Y() +
@@ -98,37 +84,18 @@ Vector3 MultiplyTranspose(const Matrix& matrix, const Vector3& vector) {
               matrix(2U, 2U) * vector.Z()};
 }
 
-/// @brief Forms the three-dimensional skew matrix of a global vector.
-Matrix Skew(const Vector3& vector) {
-  Matrix result{3U, 3U};
-  result(0U, 1U) = -vector.Z();
-  result(0U, 2U) = vector.Y();
-  result(1U, 0U) = vector.Z();
-  result(1U, 2U) = -vector.X();
-  result(2U, 0U) = -vector.Y();
-  result(2U, 1U) = vector.X();
-  return result;
-}
-
 /// @brief Scales a small dense matrix without changing its shape.
 Matrix Scale(const Matrix& matrix, const double scale) {
-  Matrix result{matrix.Rows(), matrix.Columns()};
-  for (std::size_t row = 0U; row < matrix.Rows(); ++row) {
-    for (std::size_t column = 0U; column < matrix.Columns(); ++column) {
-      result(row, column) = scale * matrix(row, column);
-    }
-  }
+  Matrix result{matrix};
+  result.Scale(scale);
   return result;
 }
 
 /// @brief Adds matching small dense matrices.
 Matrix Add(const Matrix& left, const Matrix& right) {
-  Matrix result{left.Rows(), left.Columns()};
-  for (std::size_t row = 0U; row < left.Rows(); ++row) {
-    for (std::size_t column = 0U; column < left.Columns(); ++column) {
-      result(row, column) = left(row, column) + right(row, column);
-    }
-  }
+  Matrix result{left};
+  dense_blas_internal::AxpyValues(1.0, right.Data(),
+                                  left.Rows() * left.Columns(), result.Data());
   return result;
 }
 
@@ -472,7 +439,7 @@ Result<GlobalFixedLoadContribution> AssembleGlobalFixedLoadContribution(
       return Result<GlobalFixedLoadContribution>::Failure(phi.GetStatus());
     }
     auto rotation =
-        MakeFiniteRotationState(phi.Value(), InitialFrame(*frames[node]));
+        MakeFiniteRotationState(phi.Value(), FrameMatrix(*frames[node]));
     if (!rotation.HasValue()) {
       return Result<GlobalFixedLoadContribution>::Failure(rotation.GetStatus());
     }

src/fesa/analysis/nonlinear_static_core.h

@@ -0,0 +1,16 @@
+#ifndef FESA_ANALYSIS_NONLINEAR_STATIC_CORE_H_
+#define FESA_ANALYSIS_NONLINEAR_STATIC_CORE_H_
+#include "fesa/analysis/nonlinear_static_execution_result.h"
+namespace fesa {
+class EquilibriumAlgorithm;
+class NewtonIterationLogWriter;
+class ParallelFor;
+class TangentSolver;
+/// @brief Runs the production core with caller-owned iteration policy.
+/// @note All adapters outlive this synchronous call; candidate/history stay local.
+Result<NonlinearStaticExecutionResult> ExecuteNonlinearStaticCore(
+    const Domain& domain, NewtonIterationLogWriter& log,
+    const ParallelFor& parallel_for, TangentSolver& tangent_solver,
+    EquilibriumAlgorithm& algorithm);
+}  // namespace fesa
+#endif  // FESA_ANALYSIS_NONLINEAR_STATIC_CORE_H_

src/fesa/analysis/nonlinear_static_procedure.cpp

@@ -1,11 +1,15 @@
 #include "fesa/analysis/nonlinear_static_procedure.h"
 
+#include "equilibrium_algorithm.h"
+#include "analysis/nonlinear_static_core.h"
+
 #include <algorithm>
 #include <array>
 #include <cmath>
 #include <cstddef>
 #include <cstdint>
 #include <limits>
+#include <memory>
 #include <optional>
 #include <string>
 #include <utility>
@@ -17,6 +21,7 @@
 #include "fesa/assembly/parallel_for.h"
 #include "fesa/assembly/surface_pressure_assembler.h"
 #include "fesa/constraints/essential_constraint_policy.h"
+#include "fesa/elements/element_capabilities.h"
 #include "fesa/elements/finite_rotation.h"
 #include "fesa/elements/mitc4_shell.h"
 #include "fesa/elements/nonlinear_mitc4_shell.h"
@@ -25,9 +30,16 @@
 #include "fesa/properties/shell_section.h"
 #include "fesa/solvers/linear/tangent_solver.h"
 
+#include "assembly/ordered_contribution_internal.h"
+#include "math/finite_values.h"
+#include "elements/shell_kernel_values.h"
+
 namespace fesa {
 namespace {
 
+using shell_kernel_internal::FrameMatrix;
+using math_internal::IsFinite;
+
 constexpr std::size_t kDofsPerNode = 6U;
 constexpr std::size_t kTranslationsPerNode = 3U;
 constexpr std::size_t kShellDofCount = 24U;
@@ -36,7 +48,8 @@ constexpr std::uint32_t kMaximumNewtonIterations = 100U;
 struct RuntimeShell {
   EntityIndex element_index;
   std::array<std::size_t, kShellDofCount> scatter;
-  NonlinearMitc4Shell element;
+  std::unique_ptr<NonlinearMitc4Shell> kernel;
+  std::unique_ptr<ShellTrialElement> element;
 };
 
 struct InternalAssembly {
@@ -124,16 +137,6 @@ Status RecordFailure(NewtonIterationLogWriter& log,
   return log_status.IsOk() ? failure : log_status;
 }
 
-Matrix InitialFrame(const ShellNodeInitialFrame& frame) {
-  Matrix result{3U, 3U};
-  for (std::size_t row = 0U; row < kTranslationsPerNode; ++row) {
-    result(row, 0U) = frame.tangent_a[row];
-    result(row, 1U) = frame.tangent_b[row];
-    result(row, 2U) = frame.director[row];
-  }
-  return result;
-}
-
 Result<DofManager> BuildDofManager(const Domain& domain) {
   Result<AnalysisModel> model = AnalysisModel::Create(domain);
   if (!model.HasValue()) {
@@ -239,9 +242,20 @@ Result<std::vector<RuntimeShell>> BuildRuntimeShells(const Domain& domain,
       return Result<std::vector<RuntimeShell>>::Failure(shell.GetStatus());
     }
     const EntityIndex element_index = static_cast<EntityIndex>(index);
+    auto kernel =
+        std::make_unique<NonlinearMitc4Shell>(std::move(shell.Value()));
+    auto element = std::make_unique<Mitc4TrialAdapter>(
+        ElementDofLayout{definition->SourceId(), definition->NodeIndices(),
+                         {DofComponent::kUx, DofComponent::kUy, DofComponent::kUz,
+                          DofComponent::kUrx, DofComponent::kUry, DofComponent::kUrz}},
+        *kernel);
+    auto mapped = dofs.ElementScatter(element->DofLayout());
+    if (!mapped.HasValue())
+      return Result<std::vector<RuntimeShell>>::Failure(mapped.GetStatus());
+    std::array<std::size_t, kShellDofCount> scatter{};
+    std::copy(mapped.Value().begin(), mapped.Value().end(), scatter.begin());
     shells.push_back(
-        {element_index, dofs.ShellElementScatter(element_index),
-         std::move(shell.Value())});
+        {element_index, scatter, std::move(kernel), std::move(element)});
   }
   return Result<std::vector<RuntimeShell>>::Success(std::move(shells));
 }
@@ -269,7 +283,7 @@ Status PopulateNodalKinematics(const Domain& domain,
                       trial->generalized_coordinates[first + 4U],
                       trial->generalized_coordinates[first + 5U]};
     Result<FiniteRotationState> rotation = MakeFiniteRotationState(
-        phi, InitialFrame(domain.ShellNodeInitialFrames()[node]));
+        phi, FrameMatrix(domain.ShellNodeInitialFrames()[node]));
     if (!rotation.HasValue()) {
       return rotation.GetStatus();
     }
@@ -304,26 +318,6 @@ NonlinearMitc4TrialDofs ExtractElementTrial(
   return trial;
 }
 
-bool IsFinite(const Vector& values) {
-  for (std::size_t index = 0U; index < values.Size(); ++index) {
-    if (!std::isfinite(values[index])) {
-      return false;
-    }
-  }
-  return true;
-}
-
-bool IsFinite(const Matrix& values) {
-  for (std::size_t row = 0U; row < values.Rows(); ++row) {
-    for (std::size_t column = 0U; column < values.Columns(); ++column) {
-      if (!std::isfinite(values(row, column))) {
-        return false;
-      }
-    }
-  }
-  return true;
-}
-
 Result<InternalAssembly> AssembleInternal(
     const std::vector<RuntimeShell>& shells, const DofManager& dofs,
     const Vector& coordinates, const ParallelFor& parallel_for) {
@@ -332,9 +326,8 @@ Result<InternalAssembly> AssembleInternal(
   std::vector<std::optional<Status>> failures(shells.size());
   parallel_for.Execute(shells.size(), [&](const std::size_t index) {
     Result<NonlinearMitc4InternalEquilibrium> result =
-        EvaluateInternalResidualAndTangent(shells[index].element,
-                                           ExtractElementTrial(shells[index],
-                                                               coordinates));
+        shells[index].element->EvaluateTrial(
+            ExtractElementTrial(shells[index], coordinates));
     if (!result.HasValue()) {
       failures[index] = result.GetStatus();
       return;
@@ -363,12 +356,9 @@ Result<InternalAssembly> AssembleInternal(
     }
     for (std::size_t row = 0U; row < kShellDofCount; ++row) {
       force[shells[index].scatter[row]] += local[index]->internal_residual[row];
-      for (std::size_t column = 0U; column < kShellDofCount; ++column) {
-        contributions.push_back(
-            {shells[index].scatter[row], shells[index].scatter[column],
-             local[index]->internal_tangent(row, column), index,
-             row * kShellDofCount + column});
-      }
+      assembly_internal::AppendLocalMatrixRow(
+          local[index]->internal_tangent, shells[index].scatter, row, index,
+          contributions);
     }
     for (const NonlinearMitc4RecoveryPoint& point :
          local[index]->recovery.gauss_points) {
@@ -573,19 +563,6 @@ Vector CurrentIncrementComponents(const Vector& current, const Vector& start,
   return SelectFreeComponents(difference, dofs, rotations);
 }
 
-Vector3 SpatialMoment(const Matrix& transform,
-                      const std::array<double, 3>& generalized) {
-  return {transform(0U, 0U) * generalized[0U] +
-              transform(0U, 1U) * generalized[1U] +
-              transform(0U, 2U) * generalized[2U],
-          transform(1U, 0U) * generalized[0U] +
-              transform(1U, 1U) * generalized[1U] +
-              transform(1U, 2U) * generalized[2U],
-          transform(2U, 0U) * generalized[0U] +
-              transform(2U, 1U) * generalized[1U] +
-              transform(2U, 2U) * generalized[2U]};
-}
-
 /// @brief Computes accepted-state applied-plus-reaction balance evidence.
 Result<std::array<double, 6>> GlobalEquilibrium(
     const Domain& domain, const DofManager& dofs,
@@ -634,7 +611,6 @@ Result<std::array<double, 6>> GlobalEquilibrium(
         constrained[first] ? trial.residual[first] : 0.0,
         constrained[first + 1U] ? trial.residual[first + 1U] : 0.0,
         constrained[first + 2U] ? trial.residual[first + 2U] : 0.0};
-    const Matrix transform = InverseTransposeLeftJacobianSO3(phi);
     const std::array<double, 3> applied_generalized{
         trial.external_force[first + 3U], trial.external_force[first + 4U],
         trial.external_force[first + 5U]};
@@ -642,9 +618,16 @@ Result<std::array<double, 6>> GlobalEquilibrium(
         constrained[first + 3U] ? trial.residual[first + 3U] : 0.0,
         constrained[first + 4U] ? trial.residual[first + 4U] : 0.0,
         constrained[first + 5U] ? trial.residual[first + 5U] : 0.0};
-    const Vector3 applied_moment = SpatialMoment(transform, applied_generalized);
-    const Vector3 reaction_moment =
-        SpatialMoment(transform, reaction_generalized);
+    const auto applied = SpatialMomentSO3(phi, Vector3(applied_generalized));
+    const auto reaction = SpatialMomentSO3(phi, Vector3(reaction_generalized));
+    if (!applied.HasValue() || !reaction.HasValue())
+      return Result<std::array<double, 6>>::Failure(ProcedureFailure(
+          FailureCategory::kSolver, "nonfinite-newton-data",
+          {domain.SourcePath(), 0U}, "NONLINEAR_STATIC_PROCEDURE",
+          domain.SourceContentIdentity(),
+          "Nonlinear global equilibrium balance is nonfinite."));
+    const Vector3 applied_moment = applied.Value();
+    const Vector3 reaction_moment = reaction.Value();
     applied_force_resultant = applied_force_resultant + applied_force;
     applied_moment_resultant =
         applied_moment_resultant + position.Cross(applied_force) + applied_moment;
@@ -694,11 +677,11 @@ Status ApplyIncrementConstraints(const StepDefinition& step,
   return Status::Ok();
 }
 
-AcceptedFrameState AcceptedFrame(const NonlinearAnalysisState& state,
+AcceptedFrameState AcceptedFrame(const std::uint32_t frame_index,
                                  const NonlinearTrialState& trial,
                                  const LoadFactorIncrement& increment,
                                  const std::uint32_t iteration) {
-  return {static_cast<std::uint32_t>(state.AcceptedFrames().size()),
+  return {frame_index,
           increment.increment_index,
           increment.load_factor,
           iteration,
@@ -728,6 +711,15 @@ NonlinearStaticProcedureExecutor::NonlinearStaticProcedureExecutor(
 Result<NonlinearStaticExecutionResult>
 NonlinearStaticProcedureExecutor::Execute(
     const Domain& domain, NewtonIterationLogWriter& log) const {
+  NewtonStepAlgorithm algorithm;
+  return ExecuteNonlinearStaticCore(domain, log, parallel_for_, tangent_solver_,
+                                     algorithm);
+}
+
+Result<NonlinearStaticExecutionResult> ExecuteNonlinearStaticCore(
+    const Domain& domain, NewtonIterationLogWriter& log,
+    const ParallelFor& parallel_for, TangentSolver& tangent_solver,
+    EquilibriumAlgorithm& algorithm) {
   if (domain.Steps().Size() != 1U || !domain.Steps()[0U].IsNonlinearStatic()) {
     return Result<NonlinearStaticExecutionResult>::Failure(ProcedureFailure(
         FailureCategory::kInput, "invalid-nonlinear-static-data",
@@ -782,199 +774,237 @@ NonlinearStaticProcedureExecutor::Execute(
       return Result<NonlinearStaticExecutionResult>::Failure(constraint_status);
     }
 
-    for (std::uint32_t iteration = 1U; iteration <= kMaximumNewtonIterations;
-         ++iteration) {
-      NewtonIterationLogRecord record =
-          NewLogRecord(step, increment, iteration);
-      trial.Value().increment_index = increment.increment_index;
-      trial.Value().load_factor = increment.load_factor;
-      trial.Value().is_factor_zero_baseline = false;
+    struct ShellStepCandidate {
+      AcceptedFrameState frame;
+      NewtonIterationLogRecord record;
+    };
+    const auto next_frame_index =
+        static_cast<std::uint32_t>(state.Value().AcceptedFrames().size());
+    const auto report_failure = [&](NewtonIterationLogRecord* record,
+                                    const Status& failure,
+                                    NewtonIterationStage stage) {
+      return RecordFailure(log, record, failure, stage);
+    };
+    const auto write_iteration = [&](const NewtonIterationLogRecord& record) {
+      return WriteAndFlush(log, record);
+    };
+    ShellFullNewtonStep<ShellStepCandidate> iteration_step(
+        [&](std::uint32_t iteration)
+            -> Result<std::optional<ShellStepCandidate>> {
+          NewtonIterationLogRecord record =
+              NewLogRecord(step, increment, iteration);
+          trial.Value().increment_index = increment.increment_index;
+          trial.Value().load_factor = increment.load_factor;
+          trial.Value().is_factor_zero_baseline = false;
 
-      Status kinematics = PopulateNodalKinematics(domain, &trial.Value());
-      if (!kinematics.IsOk()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(
-            RecordFailure(log, &record, kinematics,
-                          NewtonIterationStage::kKinematicsEvaluated));
-      }
-      record.last_completed_stage = NewtonIterationStage::kKinematicsEvaluated;
+          Status kinematics = PopulateNodalKinematics(domain, &trial.Value());
+          if (!kinematics.IsOk()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, kinematics,
+                               NewtonIterationStage::kKinematicsEvaluated));
+          }
+          record.last_completed_stage =
+              NewtonIterationStage::kKinematicsEvaluated;
 
-      Result<InternalAssembly> internal = AssembleInternal(
-          shells.Value(), dofs.Value(), trial.Value().generalized_coordinates,
-          parallel_for_);
-      if (!internal.HasValue()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-            log, &record, internal.GetStatus(),
-            NewtonIterationStage::kInternalAssembled));
-      }
-      record.last_completed_stage = NewtonIterationStage::kInternalAssembled;
+          Result<InternalAssembly> internal = AssembleInternal(
+              shells.Value(), dofs.Value(),
+              trial.Value().generalized_coordinates, parallel_for);
+          if (!internal.HasValue()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, internal.GetStatus(),
+                               NewtonIterationStage::kInternalAssembled));
+          }
+          record.last_completed_stage =
+              NewtonIterationStage::kInternalAssembled;
 
-      Result<GlobalFixedLoadContribution> fixed =
-          AssembleGlobalFixedLoadContribution(
-              domain, dofs.Value(), trial.Value().generalized_coordinates,
-              increment.load_factor);
-      if (!fixed.HasValue()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(
-            RecordFailure(log, &record, fixed.GetStatus(),
-                          NewtonIterationStage::kExternalAssembled));
-      }
-      Result<SurfacePressureAssemblyCandidate> pressure =
-          AssembleSurfacePressure(
-              analysis_model.Value(), dofs.Value(),
-              trial.Value().generalized_coordinates, increment.load_factor,
-              SurfacePressureConfiguration::kCurrent, parallel_for_);
-      if (!pressure.HasValue()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(
-            RecordFailure(log, &record, pressure.GetStatus(),
-                          NewtonIterationStage::kExternalAssembled));
-      }
-      Result<GlobalFixedLoadContribution> external =
-          CombineExternalContributions(fixed.Value(), pressure.Value(),
-                                       dofs.Value());
-      if (!external.HasValue()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(
-            RecordFailure(log, &record, external.GetStatus(),
-                          NewtonIterationStage::kExternalAssembled));
-      }
-      record.last_completed_stage = NewtonIterationStage::kExternalAssembled;
+          Result<GlobalFixedLoadContribution> fixed =
+              AssembleGlobalFixedLoadContribution(
+                  domain, dofs.Value(), trial.Value().generalized_coordinates,
+                  increment.load_factor);
+          if (!fixed.HasValue()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, fixed.GetStatus(),
+                               NewtonIterationStage::kExternalAssembled));
+          }
+          Result<SurfacePressureAssemblyCandidate> pressure =
+              AssembleSurfacePressure(
+                  analysis_model.Value(), dofs.Value(),
+                  trial.Value().generalized_coordinates, increment.load_factor,
+                  SurfacePressureConfiguration::kCurrent, parallel_for);
+          if (!pressure.HasValue()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, pressure.GetStatus(),
+                               NewtonIterationStage::kExternalAssembled));
+          }
+          Result<GlobalFixedLoadContribution> external =
+              CombineExternalContributions(fixed.Value(), pressure.Value(),
+                                           dofs.Value());
+          if (!external.HasValue()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, external.GetStatus(),
+                               NewtonIterationStage::kExternalAssembled));
+          }
+          record.last_completed_stage =
+              NewtonIterationStage::kExternalAssembled;
 
-      Result<Vector> residual =
-          Difference(internal.Value().force,
-                     external.Value().generalized_external_force);
-      if (!residual.HasValue()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-            log, &record, residual.GetStatus(),
-            NewtonIterationStage::kExternalAssembled));
-      }
-      Result<SparseMatrix> tangent =
-          Difference(internal.Value().tangent,
-                     external.Value().generalized_external_tangent,
-                     dofs.Value());
-      if (!tangent.HasValue()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-            log, &record, tangent.GetStatus(),
-            NewtonIterationStage::kExternalAssembled));
-      }
-      trial.Value().internal_force = std::move(internal.Value().force);
-      trial.Value().external_force =
-          std::move(external.Value().generalized_external_force);
-      trial.Value().residual = std::move(residual.Value());
-      trial.Value().reaction = trial.Value().residual;
-      trial.Value().shell_results = std::move(internal.Value().shell_rows);
-      trial.Value().physical_strain_energy =
-          internal.Value().physical_strain_energy;
-      Result<std::array<double, 6>> global_equilibrium =
-          GlobalEquilibrium(domain, dofs.Value(), trial.Value());
-      if (!global_equilibrium.HasValue()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-            log, &record, global_equilibrium.GetStatus(),
-            NewtonIterationStage::kExternalAssembled));
-      }
-      trial.Value().global_equilibrium = global_equilibrium.Value();
+          Result<Vector> residual =
+              Difference(internal.Value().force,
+                         external.Value().generalized_external_force);
+          if (!residual.HasValue()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, residual.GetStatus(),
+                               NewtonIterationStage::kExternalAssembled));
+          }
+          Result<SparseMatrix> tangent = Difference(
+              internal.Value().tangent,
+              external.Value().generalized_external_tangent, dofs.Value());
+          if (!tangent.HasValue()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, tangent.GetStatus(),
+                               NewtonIterationStage::kExternalAssembled));
+          }
+          trial.Value().internal_force = std::move(internal.Value().force);
+          trial.Value().external_force =
+              std::move(external.Value().generalized_external_force);
+          trial.Value().residual = std::move(residual.Value());
+          trial.Value().reaction = trial.Value().residual;
+          trial.Value().shell_results = std::move(internal.Value().shell_rows);
+          trial.Value().physical_strain_energy =
+              internal.Value().physical_strain_energy;
+          Result<std::array<double, 6>> global_equilibrium =
+              GlobalEquilibrium(domain, dofs.Value(), trial.Value());
+          if (!global_equilibrium.HasValue()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, global_equilibrium.GetStatus(),
+                               NewtonIterationStage::kExternalAssembled));
+          }
+          trial.Value().global_equilibrium = global_equilibrium.Value();
 
-      Result<PartitionedStiffness> partition =
-          constraints.Partition(tangent.Value(), dofs.Value());
-      if (!partition.HasValue()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-            log, &record, partition.GetStatus(),
-            NewtonIterationStage::kExternalAssembled));
-      }
-      const Status factorization = tangent_solver_.FactorizeFresh(
-          partition.Value().k_ff);
-      if (!factorization.IsOk()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-            log, &record, factorization,
-            NewtonIterationStage::kSolvedCorrection));
-      }
+          Result<PartitionedStiffness> partition =
+              constraints.Partition(tangent.Value(), dofs.Value());
+          if (!partition.HasValue()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, partition.GetStatus(),
+                               NewtonIterationStage::kExternalAssembled));
+          }
+          const Status factorization =
+              tangent_solver.FactorizeFresh(partition.Value().k_ff);
+          if (!factorization.IsOk()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, factorization,
+                               NewtonIterationStage::kSolvedCorrection));
+          }
 
-      Vector correction_rhs = constraints.GatherFree(trial.Value().residual,
-                                                      dofs.Value());
-      for (std::size_t index = 0U; index < correction_rhs.Size(); ++index) {
-        correction_rhs[index] = -correction_rhs[index];
-      }
-      Vector correction{dofs.Value().FreeDofCount()};
-      const Status solve =
-          tangent_solver_.SolveCorrection(correction_rhs, correction);
-      if (!solve.IsOk()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-            log, &record, solve, NewtonIterationStage::kSolvedCorrection));
-      }
-      record.last_completed_stage = NewtonIterationStage::kSolvedCorrection;
+          Vector correction_rhs =
+              constraints.GatherFree(trial.Value().residual, dofs.Value());
+          for (std::size_t index = 0U; index < correction_rhs.Size(); ++index) {
+            correction_rhs[index] = -correction_rhs[index];
+          }
+          Vector correction{dofs.Value().FreeDofCount()};
+          const Status solve =
+              tangent_solver.SolveCorrection(correction_rhs, correction);
+          if (!solve.IsOk()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, solve,
+                               NewtonIterationStage::kSolvedCorrection));
+          }
+          record.last_completed_stage = NewtonIterationStage::kSolvedCorrection;
 
-      const NewtonConvergenceResult convergence = EvaluateNewtonConvergence({
-          {"residual_force", SelectFreeComponents(trial.Value().residual,
-                                                    dofs.Value(), false),
-           SelectFreeComponents(trial.Value().internal_force, dofs.Value(),
-                                false),
-           SelectFreeComponents(trial.Value().external_force, dofs.Value(),
-                                false)},
-          {"residual_moment", SelectFreeComponents(trial.Value().residual,
-                                                     dofs.Value(), true),
-           SelectFreeComponents(trial.Value().internal_force, dofs.Value(),
-                                true),
-           SelectFreeComponents(trial.Value().external_force, dofs.Value(),
-                                true)},
-          {"correction_translation",
-           SelectCorrectionComponents(correction, dofs.Value(), false),
-           CurrentIncrementComponents(trial.Value().generalized_coordinates,
-                                      increment_start, dofs.Value(), false)},
-          {"correction_rotation",
-           SelectCorrectionComponents(correction, dofs.Value(), true),
-           CurrentIncrementComponents(trial.Value().generalized_coordinates,
-                                      increment_start, dofs.Value(), true)}});
-      record.force_residual = convergence.force_residual;
-      record.moment_residual = convergence.moment_residual;
-      record.translation_correction = convergence.translation_correction;
-      record.rotation_correction = convergence.rotation_correction;
-      record.combined_passed = convergence.combined_passed;
-      record.last_completed_stage = NewtonIterationStage::kConvergenceEvaluated;
+          const NewtonConvergenceResult convergence = EvaluateNewtonConvergence(
+              {{"residual_force",
+                SelectFreeComponents(trial.Value().residual, dofs.Value(),
+                                     false),
+                SelectFreeComponents(trial.Value().internal_force, dofs.Value(),
+                                     false),
+                SelectFreeComponents(trial.Value().external_force, dofs.Value(),
+                                     false)},
+               {"residual_moment",
+                SelectFreeComponents(trial.Value().residual, dofs.Value(),
+                                     true),
+                SelectFreeComponents(trial.Value().internal_force, dofs.Value(),
+                                     true),
+                SelectFreeComponents(trial.Value().external_force, dofs.Value(),
+                                     true)},
+               {"correction_translation",
+                SelectCorrectionComponents(correction, dofs.Value(), false),
+                CurrentIncrementComponents(
+                    trial.Value().generalized_coordinates, increment_start,
+                    dofs.Value(), false)},
+               {"correction_rotation",
+                SelectCorrectionComponents(correction, dofs.Value(), true),
+                CurrentIncrementComponents(
+                    trial.Value().generalized_coordinates, increment_start,
+                    dofs.Value(), true)}});
+          record.force_residual = convergence.force_residual;
+          record.moment_residual = convergence.moment_residual;
+          record.translation_correction = convergence.translation_correction;
+          record.rotation_correction = convergence.rotation_correction;
+          record.combined_passed = convergence.combined_passed;
+          record.last_completed_stage =
+              NewtonIterationStage::kConvergenceEvaluated;
 
-      if (convergence.combined_passed) {
-        const Status committed = state.Value().CommitAcceptedFrame(
-            AcceptedFrame(state.Value(), trial.Value(), increment, iteration));
-        if (!committed.IsOk()) {
-          return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-              log, &record, committed, NewtonIterationStage::kAccepted));
-        }
-        record.last_completed_stage = NewtonIterationStage::kAccepted;
-        record.transition = "accepted";
-        record.outcome = "accepted";
-        const Status log_status = WriteAndFlush(log, record);
-        if (!log_status.IsOk()) {
-          return Result<NonlinearStaticExecutionResult>::Failure(log_status);
-        }
-        break;
-      }
+          if (convergence.combined_passed) {
+            return Result<std::optional<ShellStepCandidate>>::Success(
+                ShellStepCandidate{AcceptedFrame(next_frame_index,
+                                                 trial.Value(), increment,
+                                                 iteration),
+                                   record});
+          }
 
-      if (iteration == kMaximumNewtonIterations) {
-        const Status failure = ProcedureFailure(
-            FailureCategory::kSolver, "nonlinear-nonconvergence",
-            step.Location(), "STATIC", step.Name(),
-            "The nonlinear procedure did not converge within 100 iterations.");
-        return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-            log, &record, failure,
-            NewtonIterationStage::kConvergenceEvaluated));
-      }
+          if (iteration == kMaximumNewtonIterations) {
+            const Status failure = ProcedureFailure(
+                FailureCategory::kSolver, "nonlinear-nonconvergence",
+                step.Location(), "STATIC", step.Name(),
+                "The nonlinear procedure did not converge within 100 "
+                "iterations.");
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                report_failure(&record, failure,
+                               NewtonIterationStage::kConvergenceEvaluated));
+          }
 
-      for (std::size_t equation = 0U; equation < dofs.Value().FreeDofs().size();
-           ++equation) {
-        const std::size_t full_dof = dofs.Value().FreeDofs()[equation];
-        trial.Value().generalized_coordinates[full_dof] += correction[equation];
-        if (!std::isfinite(trial.Value().generalized_coordinates[full_dof])) {
-          const Status failure = ProcedureFailure(
-              FailureCategory::kSolver, "nonfinite-newton-data", {},
-              "NONLINEAR_STATIC_PROCEDURE", std::to_string(full_dof),
-              "A nonlinear free-coordinate correction is nonfinite.");
-          return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
-              log, &record, failure, NewtonIterationStage::kSolvedCorrection));
-        }
-      }
-      record.transition = "continue";
-      record.outcome = "not-converged";
-      const Status log_status = WriteAndFlush(log, record);
-      if (!log_status.IsOk()) {
-        return Result<NonlinearStaticExecutionResult>::Failure(log_status);
-      }
+          for (std::size_t equation = 0U;
+               equation < dofs.Value().FreeDofs().size(); ++equation) {
+            const std::size_t full_dof = dofs.Value().FreeDofs()[equation];
+            trial.Value().generalized_coordinates[full_dof] +=
+                correction[equation];
+            if (!std::isfinite(
+                    trial.Value().generalized_coordinates[full_dof])) {
+              const Status failure = ProcedureFailure(
+                  FailureCategory::kSolver, "nonfinite-newton-data", {},
+                  "NONLINEAR_STATIC_PROCEDURE", std::to_string(full_dof),
+                  "A nonlinear free-coordinate correction is nonfinite.");
+              return Result<std::optional<ShellStepCandidate>>::Failure(
+                  report_failure(&record, failure,
+                                 NewtonIterationStage::kSolvedCorrection));
+            }
+          }
+          record.transition = "continue";
+          record.outcome = "not-converged";
+          const Status log_status = write_iteration(record);
+          if (!log_status.IsOk()) {
+            return Result<std::optional<ShellStepCandidate>>::Failure(
+                log_status);
+          }
+          return Result<std::optional<ShellStepCandidate>>::Success(
+              std::nullopt);
+        },
+        kMaximumNewtonIterations);
+    const Status solved = iteration_step.Solve(algorithm);
+    if (!solved.IsOk())
+      return Result<NonlinearStaticExecutionResult>::Failure(solved);
+    auto candidate = iteration_step.TakeCandidate();
+    auto& record = candidate.record;
+    const Status committed = state.Value().CommitAcceptedFrame(candidate.frame);
+    if (!committed.IsOk()) {
+      return Result<NonlinearStaticExecutionResult>::Failure(RecordFailure(
+          log, &record, committed, NewtonIterationStage::kAccepted));
     }
+    record.last_completed_stage = NewtonIterationStage::kAccepted;
+    record.transition = "accepted";
+    record.outcome = "accepted";
+    const Status log_status = WriteAndFlush(log, record);
+    if (!log_status.IsOk())
+      return Result<NonlinearStaticExecutionResult>::Failure(log_status);
   }
 
   std::vector<Diagnostic> diagnostics = domain.Warnings();
@@ -983,4 +1013,4 @@ NonlinearStaticProcedureExecutor::Execute(
       {std::move(state.Value()), std::move(diagnostics)});
 }
 
-}  // namespace fesa
+} // namespace fesa

src/fesa/analysis/prepared_analysis.cpp

@@ -1,7 +1,10 @@
 #include "fesa/analysis/prepared_analysis.h"
 
+#include <memory>
 #include <utility>
 
+#include "analysis_procedures.h"
+
 #include "fesa/analysis/analysis_model.h"
 #include "fesa/analysis/hht_dynamic_procedure.h"
 #include "fesa/analysis/linear_frequency_procedure.h"
@@ -9,15 +12,13 @@
 #include "fesa/analysis/newton_iteration_log.h"
 #include "fesa/analysis/nonlinear_static_procedure.h"
 #include "fesa/analysis/solid_frequency_procedure.h"
+#include "fesa/analysis/solid_hht_dynamic_procedure.h"
+#include "fesa/analysis/solid_static_procedure.h"
+#include "fesa/analysis/transient_heat_procedure.h"
 #include "fesa/app/output_paths.h"
 #include "fesa/io/abaqus/domain_mapper.h"
 #include "fesa/io/abaqus/input_reader.h"
-#include "fesa/results/dynamic_results_writer.h"
-#include "fesa/results/eigen_results_writer.h"
-#include "fesa/results/nonlinear_results_writer.h"
-#include "fesa/results/results_writer.h"
-#include "fesa/results/solid_results_writer.h"
-#include "fesa/results/thermal_results_writer.h"
+#include "fesa/results/prepared_results_writer.h"
 
 namespace fesa {
 
@@ -39,6 +40,185 @@ Result<PreparedAnalysisInput> PrepareAnalysisInput(
   return Result<PreparedAnalysisInput>::Success(std::move(prepared));
 }
 
+namespace {
+
+enum class ProcedureKind {
+  kLinearStatic,
+  kNonlinearStatic,
+  kLinearFrequency,
+  kHhtDynamic,
+  kSolidStatic,
+  kSolidFrequency,
+  kSolidHhtDynamic,
+  kTransientHeat
+};
+
+// Keep procedure precedence and step-count diagnostics common to both APIs.
+Result<ProcedureKind> SelectProcedure(const Domain& domain) {
+  if (domain.ThermalStep() != nullptr)
+    return Result<ProcedureKind>::Success(ProcedureKind::kTransientHeat);
+  if (domain.Steps().Size() != 1U) {
+    return Result<ProcedureKind>::Failure(Status::Failure(
+        FailureCategory::kInput,
+        {{Severity::kError,
+          "invalid-analysis-step-count",
+          {},
+          "*STEP",
+          {},
+          "Prepared analysis requires exactly one analysis step."}}));
+  }
+  if (domain.IsSolid()) {
+    if (domain.Dynamic() != nullptr)
+      return Result<ProcedureKind>::Success(ProcedureKind::kSolidHhtDynamic);
+    if (domain.Steps()[0U].IsFrequency())
+      return Result<ProcedureKind>::Success(ProcedureKind::kSolidFrequency);
+    return Result<ProcedureKind>::Success(ProcedureKind::kSolidStatic);
+  }
+  if (domain.Dynamic() != nullptr)
+    return Result<ProcedureKind>::Success(ProcedureKind::kHhtDynamic);
+  if (domain.Steps()[0U].IsFrequency())
+    return Result<ProcedureKind>::Success(ProcedureKind::kLinearFrequency);
+  if (domain.Steps()[0U].IsNonlinearStatic())
+    return Result<ProcedureKind>::Success(ProcedureKind::kNonlinearStatic);
+  return Result<ProcedureKind>::Success(ProcedureKind::kLinearStatic);
+}
+
+template <typename Payload>
+Result<PreparedAnalysisOutcome> Completed(Result<Payload> result) {
+  if (!result.HasValue())
+    return Result<PreparedAnalysisOutcome>::Failure(result.GetStatus());
+  return Result<PreparedAnalysisOutcome>::Success(
+      PreparedAnalysisOutcome{std::move(result.Value())});
+}
+
+Result<PreparedAnalysisOutcome>
+MissingExecutor(const char* code, const char* keyword, const char* message) {
+  return Result<PreparedAnalysisOutcome>::Failure(
+      Status::Failure(FailureCategory::kSolver,
+                      {{Severity::kError, code, {}, keyword, {}, message}}));
+}
+
+} // namespace
+
+Result<PreparedAnalysisOutcome>
+LinearStaticProcedure::Execute(const Domain& domain) {
+  return Completed(executor_.Execute(domain));
+}
+
+Result<PreparedAnalysisOutcome>
+NonlinearStaticProcedure::Execute(const Domain& domain) {
+  return Completed(executor_.Execute(domain, log_));
+}
+
+Result<PreparedAnalysisOutcome>
+LinearFrequencyProcedure::Execute(const Domain& domain) {
+  return Completed(executor_.Execute(domain));
+}
+
+Result<PreparedAnalysisOutcome>
+HhtDynamicProcedure::Execute(const Domain& domain) {
+  return Completed(executor_.Execute(domain, log_));
+}
+
+Result<PreparedAnalysisOutcome>
+SolidStaticProcedure::Execute(const Domain& domain) {
+  SolidStaticState state;
+  const Status execution = executor_.ExecuteInto(domain, state);
+  for (const auto& record : state.IterationRecords()) {
+    const Status written = log_.Write(record, domain.Steps()[0U].Name());
+    if (!written.IsOk())
+      return Result<PreparedAnalysisOutcome>::Failure(written);
+  }
+  if (!execution.IsOk())
+    return Result<PreparedAnalysisOutcome>::Failure(execution);
+  return Result<PreparedAnalysisOutcome>::Success(PreparedAnalysisOutcome{
+      SolidStaticExecutionResult{std::move(state), domain.Warnings()}});
+}
+
+Result<PreparedAnalysisOutcome>
+SolidFrequencyProcedure::Execute(const Domain& domain) {
+  return Completed(executor_.Execute(domain));
+}
+
+Result<PreparedAnalysisOutcome>
+SolidHhtDynamicProcedure::Execute(const Domain& domain) {
+  auto model = AnalysisModel::Create(domain);
+  if (!model.HasValue())
+    return Result<PreparedAnalysisOutcome>::Failure(model.GetStatus());
+  auto dofs = DofManager::Create(model.Value());
+  if (!dofs.HasValue())
+    return Result<PreparedAnalysisOutcome>::Failure(dofs.GetStatus());
+  auto state = SolidDynamicAnalysisState::Create(domain, dofs.Value());
+  if (!state.HasValue())
+    return Result<PreparedAnalysisOutcome>::Failure(state.GetStatus());
+  const Status execution = executor_.ExecuteInto(domain, state.Value());
+  for (const auto& record : state.Value().IterationRecords()) {
+    const Status written = log_.Write(record);
+    if (!written.IsOk())
+      return Result<PreparedAnalysisOutcome>::Failure(written);
+  }
+  if (!execution.IsOk())
+    return Result<PreparedAnalysisOutcome>::Failure(execution);
+  return Result<PreparedAnalysisOutcome>::Success(
+      PreparedAnalysisOutcome{SolidDynamicExecutionResult{
+          std::move(dofs.Value()), std::move(state.Value())}});
+}
+
+Result<PreparedAnalysisOutcome>
+TransientHeatProcedure::Execute(const Domain& domain) {
+  return Completed(executor_.Execute(domain));
+}
+
+Result<std::unique_ptr<AnalysisProcedure>> CreateAnalysisProcedure(
+    const Domain& domain, const ParallelFor& parallel_for,
+    LinearSolver& linear_solver, TangentSolver& tangent_solver,
+    const EigenSolver& eigen_solver, NewtonIterationLogWriter& log) {
+  const auto kind = SelectProcedure(domain);
+  if (!kind.HasValue())
+    return Result<std::unique_ptr<AnalysisProcedure>>::Failure(
+        kind.GetStatus());
+  std::unique_ptr<AnalysisProcedure> procedure;
+  switch (kind.Value()) {
+  case ProcedureKind::kLinearStatic:
+    procedure =
+        std::make_unique<LinearStaticProcedure>(parallel_for, linear_solver);
+    break;
+  case ProcedureKind::kNonlinearStatic:
+    procedure = std::make_unique<NonlinearStaticProcedure>(parallel_for,
+                                                           tangent_solver, log);
+    break;
+  case ProcedureKind::kLinearFrequency:
+    procedure = std::make_unique<LinearFrequencyProcedure>(eigen_solver);
+    break;
+  case ProcedureKind::kHhtDynamic:
+    procedure = std::make_unique<HhtDynamicProcedure>(
+        parallel_for, linear_solver, tangent_solver, log);
+    break;
+  case ProcedureKind::kSolidStatic:
+    procedure = std::make_unique<SolidStaticProcedure>(
+        parallel_for, linear_solver, tangent_solver, log);
+    break;
+  case ProcedureKind::kSolidFrequency:
+    procedure = std::make_unique<SolidFrequencyProcedure>(eigen_solver);
+    break;
+  case ProcedureKind::kSolidHhtDynamic:
+    procedure = std::make_unique<SolidHhtDynamicProcedure>(
+        parallel_for, linear_solver, tangent_solver, log);
+    break;
+  case ProcedureKind::kTransientHeat:
+    procedure =
+        std::make_unique<TransientHeatProcedure>(parallel_for, linear_solver);
+    break;
+  }
+  return Result<std::unique_ptr<AnalysisProcedure>>::Success(
+      std::move(procedure));
+}
+
+Result<PreparedAnalysisOutcome>
+ExecutePreparedAnalysis(const Domain& domain, AnalysisProcedure& procedure) {
+  return procedure.Execute(domain);
+}
+
 Result<PreparedAnalysisOutcome> ExecutePreparedAnalysis(
     const Domain& domain, LinearStaticProcedureExecutor& linear_executor,
     NonlinearStaticProcedureExecutor& nonlinear_executor,
@@ -49,133 +229,59 @@ Result<PreparedAnalysisOutcome> ExecutePreparedAnalysis(
     const SolidStaticProcedureExecutor* solid_static_executor,
     const SolidFrequencyProcedureExecutor* solid_frequency_executor,
     const SolidHhtDynamicProcedureExecutor* solid_dynamic_executor) {
-  if (domain.ThermalStep() != nullptr) {
-    if (thermal_executor == nullptr) {
-      return Result<PreparedAnalysisOutcome>::Failure(
-          Status::Failure(FailureCategory::kSolver,
-                          {{Severity::kError,
-                            "missing-thermal-executor",
-                            {},
-                            "HEAT TRANSFER",
-                            {},
-                            "Thermal execution adapter is required."}}));
-    }
-    auto thermal = thermal_executor->Execute(domain);
-    if (!thermal.HasValue()) {
-      return Result<PreparedAnalysisOutcome>::Failure(thermal.GetStatus());
-    }
-    return Result<PreparedAnalysisOutcome>::Success(
-        PreparedAnalysisOutcome{std::move(thermal.Value())});
-  }
-  if (domain.Steps().Size() != 1U) {
-    return Result<PreparedAnalysisOutcome>::Failure(Status::Failure(
-        FailureCategory::kInput,
-        {{Severity::kError,
-          "invalid-analysis-step-count",
-          {},
-          "*STEP",
-          {},
-          "Prepared analysis requires exactly one analysis step."}}));
-  }
-
-  if (domain.IsSolid()) {
-    const auto missing = []() {
-      return Result<PreparedAnalysisOutcome>::Failure(Status::Failure(
-          FailureCategory::kSolver,
-          {{Severity::kError,
-            "missing-solid-executor",
-            {},
-            "",
-            {},
-            "The selected Solid execution adapter is required."}}));
-    };
-    if (domain.Dynamic() != nullptr) {
-      if (solid_dynamic_executor == nullptr) return missing();
-      auto model = AnalysisModel::Create(domain);
-      if (!model.HasValue())
-        return Result<PreparedAnalysisOutcome>::Failure(model.GetStatus());
-      auto dofs = DofManager::Create(model.Value());
-      if (!dofs.HasValue())
-        return Result<PreparedAnalysisOutcome>::Failure(dofs.GetStatus());
-      auto state = SolidDynamicAnalysisState::Create(domain, dofs.Value());
-      if (!state.HasValue())
-        return Result<PreparedAnalysisOutcome>::Failure(state.GetStatus());
-      const Status execution =
-          solid_dynamic_executor->ExecuteInto(domain, state.Value());
-      for (const auto& record : state.Value().IterationRecords()) {
-        const Status written = log.Write(record);
-        if (!written.IsOk())
-          return Result<PreparedAnalysisOutcome>::Failure(written);
-      }
-      if (!execution.IsOk())
-        return Result<PreparedAnalysisOutcome>::Failure(execution);
-      return Result<PreparedAnalysisOutcome>::Success(
-          PreparedAnalysisOutcome{SolidDynamicExecutionResult{
-              std::move(dofs.Value()), std::move(state.Value())}});
-    }
-    if (domain.Steps()[0U].IsFrequency()) {
-      if (solid_frequency_executor == nullptr) return missing();
-      auto result = solid_frequency_executor->Execute(domain);
-      if (!result.HasValue())
-        return Result<PreparedAnalysisOutcome>::Failure(result.GetStatus());
-      return Result<PreparedAnalysisOutcome>::Success(
-          PreparedAnalysisOutcome{std::move(result.Value())});
-    }
-    if (solid_static_executor == nullptr) return missing();
-    SolidStaticState state;
-    const Status execution = solid_static_executor->ExecuteInto(domain, state);
-    for (const auto& record : state.IterationRecords()) {
-      const Status written = log.Write(record, domain.Steps()[0U].Name());
-      if (!written.IsOk())
-        return Result<PreparedAnalysisOutcome>::Failure(written);
-    }
-    if (!execution.IsOk())
-      return Result<PreparedAnalysisOutcome>::Failure(execution);
-    return Result<PreparedAnalysisOutcome>::Success(PreparedAnalysisOutcome{
-        SolidStaticExecutionResult{std::move(state), domain.Warnings()}});
-  }
-
-  if (domain.Dynamic() != nullptr) {
+  const auto kind = SelectProcedure(domain);
+  if (!kind.HasValue())
+    return Result<PreparedAnalysisOutcome>::Failure(kind.GetStatus());
+  std::unique_ptr<AnalysisProcedure> procedure;
+  switch (kind.Value()) {
+  case ProcedureKind::kLinearStatic:
+    procedure = std::make_unique<LinearStaticProcedure>(linear_executor);
+    break;
+  case ProcedureKind::kNonlinearStatic:
+    procedure =
+        std::make_unique<NonlinearStaticProcedure>(nonlinear_executor, log);
+    break;
+  case ProcedureKind::kLinearFrequency:
+    procedure = std::make_unique<LinearFrequencyProcedure>(frequency_executor);
+    break;
+  case ProcedureKind::kHhtDynamic:
     if (dynamic_executor == nullptr)
-      return Result<PreparedAnalysisOutcome>::Failure(
-          Status::Failure(FailureCategory::kSolver,
-                          {{Severity::kError,
-                            "missing-dynamic-executor",
-                            {},
-                            "DYNAMIC",
-                            {},
-                            "Dynamic execution adapter is required."}}));
-    auto dynamic = dynamic_executor->Execute(domain, log);
-    if (!dynamic.HasValue())
-      return Result<PreparedAnalysisOutcome>::Failure(dynamic.GetStatus());
-    return Result<PreparedAnalysisOutcome>::Success(
-        PreparedAnalysisOutcome{std::move(dynamic.Value())});
+      return MissingExecutor("missing-dynamic-executor", "DYNAMIC",
+                             "Dynamic execution adapter is required.");
+    procedure = std::make_unique<HhtDynamicProcedure>(*dynamic_executor, log);
+    break;
+  case ProcedureKind::kSolidStatic:
+    if (solid_static_executor == nullptr)
+      return MissingExecutor(
+          "missing-solid-executor", "",
+          "The selected Solid execution adapter is required.");
+    procedure =
+        std::make_unique<SolidStaticProcedure>(*solid_static_executor, log);
+    break;
+  case ProcedureKind::kSolidFrequency:
+    if (solid_frequency_executor == nullptr)
+      return MissingExecutor(
+          "missing-solid-executor", "",
+          "The selected Solid execution adapter is required.");
+    procedure =
+        std::make_unique<SolidFrequencyProcedure>(*solid_frequency_executor);
+    break;
+  case ProcedureKind::kSolidHhtDynamic:
+    if (solid_dynamic_executor == nullptr)
+      return MissingExecutor(
+          "missing-solid-executor", "",
+          "The selected Solid execution adapter is required.");
+    procedure = std::make_unique<SolidHhtDynamicProcedure>(
+        *solid_dynamic_executor, log);
+    break;
+  case ProcedureKind::kTransientHeat:
+    if (thermal_executor == nullptr)
+      return MissingExecutor("missing-thermal-executor", "HEAT TRANSFER",
+                             "Thermal execution adapter is required.");
+    procedure = std::make_unique<TransientHeatProcedure>(*thermal_executor);
+    break;
   }
-  if (domain.Steps()[0U].IsFrequency()) {
-    auto eigen = frequency_executor.Execute(domain);
-    if (!eigen.HasValue()) {
-      return Result<PreparedAnalysisOutcome>::Failure(eigen.GetStatus());
-    }
-    return Result<PreparedAnalysisOutcome>::Success(
-        PreparedAnalysisOutcome{std::move(eigen.Value())});
-  }
-
-  if (domain.Steps()[0U].IsNonlinearStatic()) {
-    Result<NonlinearStaticExecutionResult> nonlinear =
-        nonlinear_executor.Execute(domain, log);
-    if (!nonlinear.HasValue()) {
-      return Result<PreparedAnalysisOutcome>::Failure(nonlinear.GetStatus());
-    }
-    return Result<PreparedAnalysisOutcome>::Success(
-        PreparedAnalysisOutcome{std::move(nonlinear.Value())});
-  }
-
-  Result<LinearStaticExecutionResult> linear = linear_executor.Execute(domain);
-  if (!linear.HasValue()) {
-    return Result<PreparedAnalysisOutcome>::Failure(linear.GetStatus());
-  }
-  return Result<PreparedAnalysisOutcome>::Success(
-      PreparedAnalysisOutcome{std::move(linear.Value())});
+  return ExecutePreparedAnalysis(domain, *procedure);
 }
 
 Status FinalizePreparedAnalysisResult(
@@ -185,68 +291,10 @@ Status FinalizePreparedAnalysisResult(
     NonlinearResultsWriter& nonlinear_writer, EigenResultsWriter& eigen_writer,
     DynamicResultsWriter* dynamic_writer, ThermalResultsWriter* thermal_writer,
     SolidResultsWriter* solid_writer) {
-  if (std::holds_alternative<SolidStaticExecutionResult>(outcome) ||
-      std::holds_alternative<SolidFrequencyState>(outcome) ||
-      std::holds_alternative<SolidDynamicExecutionResult>(outcome)) {
-    if (solid_writer == nullptr)
-      return Status::Failure(FailureCategory::kOutput,
-                             {{Severity::kError,
-                               "missing-solid-writer",
-                               {},
-                               "",
-                               {},
-                               "Solid result writer is required."}});
-    if (const auto* result = std::get_if<SolidStaticExecutionResult>(&outcome))
-      return solid_writer->Write(paths.results_path, domain, result->state,
-                                 diagnostics);
-    if (const auto* result = std::get_if<SolidFrequencyState>(&outcome))
-      return solid_writer->Write(paths.results_path, domain, *result,
-                                 diagnostics);
-    return solid_writer->Write(
-        paths.results_path, domain,
-        std::get<SolidDynamicExecutionResult>(outcome).state, diagnostics);
-  }
-  if (std::holds_alternative<ThermalExecutionResult>(outcome)) {
-    if (thermal_writer == nullptr) {
-      return Status::Failure(FailureCategory::kOutput,
-                             {{Severity::kError,
-                               "missing-thermal-writer",
-                               {},
-                               "HEAT TRANSFER",
-                               {},
-                               "Thermal result writer is required."}});
-    }
-    return thermal_writer->Write(
-        paths.results_path, domain,
-        std::get<ThermalExecutionResult>(outcome).state, diagnostics);
-  }
-  if (std::holds_alternative<DynamicExecutionResult>(outcome)) {
-    if (dynamic_writer == nullptr)
-      return Status::Failure(FailureCategory::kOutput,
-                             {{Severity::kError,
-                               "missing-dynamic-writer",
-                               {},
-                               "DYNAMIC",
-                               {},
-                               "Dynamic result writer is required."}});
-    return dynamic_writer->Write(
-        paths.results_path, domain,
-        std::get<DynamicExecutionResult>(outcome).state, diagnostics);
-  }
-  if (std::holds_alternative<EigenAnalysisState>(outcome)) {
-    return eigen_writer.Write(paths.results_path, domain,
-                              std::get<EigenAnalysisState>(outcome),
-                              diagnostics);
-  }
-  if (std::holds_alternative<LinearStaticExecutionResult>(outcome)) {
-    return linear_writer.Write(
-        paths.results_path, domain,
-        std::get<LinearStaticExecutionResult>(outcome).state, diagnostics);
-  }
-
-  return nonlinear_writer.Write(
-      paths.results_path, domain,
-      std::get<NonlinearStaticExecutionResult>(outcome).state, diagnostics);
+  return WritePreparedAnalysisResult(
+      paths.results_path, domain, outcome, diagnostics, linear_writer,
+      nonlinear_writer, eigen_writer, dynamic_writer, thermal_writer,
+      solid_writer);
 }
 
 }  // namespace fesa

src/fesa/analysis/shell_state_inventory.h

@@ -0,0 +1,25 @@
+#ifndef FESA_ANALYSIS_SHELL_STATE_INVENTORY_H_
+#define FESA_ANALYSIS_SHELL_STATE_INVENTORY_H_
+
+#include <cstddef>
+#include <vector>
+
+#include "fesa/elements/element_definition.h"
+#include "fesa/model/domain.h"
+
+namespace fesa::analysis_internal {
+
+/// @brief Collects unified MITC4 element indices in stable Domain order.
+inline std::vector<EntityIndex> ShellElementOrder(const Domain& domain) {
+  std::vector<EntityIndex> order;
+  for (std::size_t index = 0U; index < domain.Elements().Size(); ++index) {
+    if (domain.Elements()[index].Kind() == ElementDefinitionKind::kMitc4Shell) {
+      order.push_back(static_cast<EntityIndex>(index));
+    }
+  }
+  return order;
+}
+
+}  // namespace fesa::analysis_internal
+
+#endif  // FESA_ANALYSIS_SHELL_STATE_INVENTORY_H_

src/fesa/analysis/solid_dynamic_analysis_state.cpp

@@ -1,13 +1,15 @@
 #include "fesa/analysis/solid_dynamic_analysis_state.h"
 
-#include <algorithm>
 #include <cmath>
 #include <stdexcept>
 #include <string>
 
+#include "fesa/core/source_identity.h"
 #include "fesa/elements/element_factory.h"
 #include "fesa/elements/hex8_element.h"
+#include "fesa/model/domain.h"
 #include "math/high_low_arithmetic.h"
+#include "math/finite_values.h"
 
 namespace fesa {
 namespace {
@@ -24,8 +26,7 @@ Status Failure(const std::string& message) {
 /// @brief Checks a physical record without replacing nonfinite quantities.
 template <std::size_t N>
 bool Finite(const std::array<double, N>& values) {
-  return std::all_of(values.begin(), values.end(),
-                     [](double x) { return std::isfinite(x); });
+  return math_internal::IsFinite(values);
 }
 bool ValidPair(double high, double low) {
   const math_internal::HighLow value(high, low);
@@ -44,12 +45,6 @@ bool ValidPair(const std::array<double, N>& high,
     if (!ValidPair(high[i], low[i])) return false;
   return true;
 }
-/// @brief Preserves canonical and raw source identity independently of indices.
-bool SameId(const SourceEntityId& a, const SourceEntityId& b) {
-  return a.instance_name == b.instance_name &&
-         a.source_label == b.source_label &&
-         a.source_label_text == b.source_label_text;
-}
 }  // namespace
 
 Result<SolidDynamicAnalysisState> SolidDynamicAnalysisState::Create(
@@ -83,7 +78,7 @@ Result<SolidDynamicAnalysisState> SolidDynamicAnalysisState::Create(
     auto runtime = factory.Create(domain.Elements()[e], domain);
     if (!runtime.HasValue())
       return Result<SolidDynamicAnalysisState>::Failure(runtime.GetStatus());
-    const auto* solid = dynamic_cast<const Hex8Element*>(runtime.Value().get());
+    auto solid = factory.BindSolidTrial(*runtime.Value());
     if (solid == nullptr)
       return Result<SolidDynamicAnalysisState>::Failure(Failure(
           "Dynamic Solid inventory contains a different element family."));
@@ -117,7 +112,7 @@ Status SolidDynamicAnalysisState::CommitAcceptedFrame(
   }
   for (std::size_t n = 0; n < source_ids_.size(); ++n)
     if (f.nodal_internal_order[n] != n ||
-        !SameId(f.nodal_source_ids[n], source_ids_[n]))
+        !SourceIdentityEquals(f.nodal_source_ids[n], source_ids_[n]))
       return Failure("Solid nodal source identity differs from its inventory.");
   const std::array<const Vector*, 10> high{
       &f.displacement,   &f.velocity,

src/fesa/analysis/solid_frequency_procedure.cpp

@@ -18,6 +18,7 @@
 #include "fesa/elements/hex8_element.h"
 #include "fesa/fem/dof_manager.h"
 #include "fesa/math/sparse_matrix.h"
+#include "fesa/solvers/eigen/mkl_feast_eigen_solver.h"
 #include "fesa/math/vector.h"
 #include "fesa/model/domain.h"
 
@@ -50,7 +51,8 @@ double Ratio(double numerator, double denominator) {
   return numerator / denominator;
 }
 /// @brief Builds an immutable candidate; all returns precede public commit.
-Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
+Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain,
+                                          const EigenSolver& solver) {
   const auto* frequency = domain.Frequency();
   if (!domain.IsSolid() || frequency == nullptr ||
       frequency->requested_mode_count <= 0)
@@ -76,6 +78,7 @@ Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
   }
   ElementFactory factory;
   std::vector<std::unique_ptr<Element>> owned;
+  std::vector<std::unique_ptr<SolidTrialElement>> trials;
   ElementView view;
   for (const auto index : model.Value().ActiveElements()) {
     const auto& definition = domain.Elements()[index];
@@ -87,11 +90,13 @@ Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
     auto element = factory.Create(definition, domain);
     if (!element.HasValue())
       return Result<SolidFrequencyState>::Failure(element.GetStatus());
-    if (dynamic_cast<const Hex8Element*>(element.Value().get()) == nullptr)
+    auto trial = factory.BindSolidTrial(*element.Value());
+    if (trial == nullptr)
       return Result<SolidFrequencyState>::Failure(
           Failure("unsupported-frequency-element", "Only C3D8 is supported."));
     view.emplace_back(*element.Value());
     owned.push_back(std::move(element.Value()));
+    trials.push_back(std::move(trial));
   }
   DofManager dofs;
   const Status mapping = dofs.Build(model.Value(), view);
@@ -121,7 +126,7 @@ Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
   std::vector<std::size_t> additions_by_dof(dofs.FullDofCount(), 0U);
   constexpr double eps = std::numeric_limits<double>::epsilon();
   for (std::size_t e = 0; e < owned.size(); ++e) {
-    const auto& hex = static_cast<const Hex8Element&>(*owned[e]);
+    const auto& hex = *trials[e];
     auto mass = hex.ComputeMass();
     if (!mass.HasValue())
       return Result<SolidFrequencyState>::Failure(mass.GetStatus());
@@ -220,7 +225,7 @@ Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
     return Result<SolidFrequencyState>::Failure(
         Failure("invalid-solid-eigen-scale",
                 "A positive finite classification scale is required."));
-  auto backend = MklFeastEigenSolver{}.SolveGeneralized(k, m, requested,
+  auto backend = solver.SolveGeneralized(k, m, requested,
                                                         mass_lower, scale);
   if (!backend.HasValue())
     return Result<SolidFrequencyState>::Failure(backend.GetStatus());
@@ -269,11 +274,11 @@ Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
                     "Normalized modal vector is not finite."));
     }
     mv = m.Multiply(vector);
-    const Vector kv = k.Multiply(vector);
+    Vector kv = k.Multiply(vector);
     const double lambda = state.backend.eigenvalues[c];
     const double modal_mass = vector.Dot(mv);
     const double energy = vector.Dot(kv);
-    Vector residual = kv;
+    Vector residual = std::move(kv);
     residual.Axpy(-lambda, mv);
     const double norm_phi = vector.Norm();
     const double residual_norm = residual.Norm();
@@ -355,7 +360,8 @@ Result<SolidFrequencyState> ExecuteCandidate(const Domain& domain) {
 Result<SolidFrequencyState> SolidFrequencyProcedureExecutor::Execute(
     const Domain& domain) const {
   try {
-    auto result = ExecuteCandidate(domain);
+    const MklFeastEigenSolver default_solver;
+    auto result = ExecuteCandidate(domain, solver_ ? *solver_ : default_solver);
     if (result.HasValue()) return result;
     auto diagnostics = result.GetStatus().Diagnostics();
     for (auto& diagnostic : diagnostics)

src/fesa/analysis/solid_hht_core.h

@@ -0,0 +1,20 @@
+#ifndef FESA_ANALYSIS_SOLID_HHT_CORE_H_
+#define FESA_ANALYSIS_SOLID_HHT_CORE_H_
+#include "fesa/core/status.h"
+namespace fesa {
+namespace detail { class SolidHhtIntegrator; }
+class Domain;
+class SolidDynamicAnalysisState;
+class ParallelFor;
+class LinearSolver;
+class TangentSolver;
+class EquilibriumAlgorithm;
+/// @brief Runs the complete production core with borrowed iteration policy.
+/// @note Adapters outlive this synchronous call; history remains state-owned.
+Status ExecuteSolidHhtCore(
+    const Domain& domain, SolidDynamicAnalysisState& state, double alpha,
+    const ParallelFor& parallel_for, LinearSolver& mass_solver,
+    TangentSolver& tangent_solver, const detail::SolidHhtIntegrator& integrator,
+    EquilibriumAlgorithm& algorithm);
+}  // namespace fesa
+#endif  // FESA_ANALYSIS_SOLID_HHT_CORE_H_

src/fesa/analysis/solid_hht_dynamic_procedure.cpp

@@ -1,5 +1,9 @@
 #include "fesa/analysis/solid_hht_dynamic_procedure.h"
 
+#include "equilibrium_algorithm.h"
+#include "analysis/solid_hht_core.h"
+#include "solid_hht_integrator.h"
+
 #include <algorithm>
 #include <array>
 #include <cmath>
@@ -85,7 +89,7 @@ Status CheckArithmeticEnvironment(const Domain& domain) {
 /// @brief Owns immutable kernels and the stable full-space translation scatter.
 struct RuntimeSolid {
   std::unique_ptr<Element> owner;
-  const Hex8Element* solid;
+  std::unique_ptr<SolidTrialElement> solid;
   std::vector<std::size_t> scatter;
 };
 /// @brief Creates checked kernels in declaration order, with no mutable element
@@ -98,7 +102,7 @@ Result<std::vector<RuntimeSolid>> BuildSolids(const Domain& domain,
     auto owner = factory.Create(domain.Elements()[e], domain);
     if (!owner.HasValue())
       return Result<std::vector<RuntimeSolid>>::Failure(owner.GetStatus());
-    const auto* solid = dynamic_cast<const Hex8Element*>(owner.Value().get());
+    auto solid = factory.BindSolidTrial(*owner.Value());
     if (solid == nullptr)
       return Result<std::vector<RuntimeSolid>>::Failure(
           Failure(domain, "solid-dynamic-element-family",
@@ -107,7 +111,7 @@ Result<std::vector<RuntimeSolid>> BuildSolids(const Domain& domain,
     if (!scatter.HasValue())
       return Result<std::vector<RuntimeSolid>>::Failure(scatter.GetStatus());
     solids.push_back(
-        {std::move(owner.Value()), solid, std::move(scatter.Value())});
+        {std::move(owner.Value()), std::move(solid), std::move(scatter.Value())});
   }
   return Result<std::vector<RuntimeSolid>>::Success(std::move(solids));
 }
@@ -239,7 +243,7 @@ Result<double> ReferenceLength(const Domain& domain) {
                 "Reference length is not finite positive."));
   return Result<double>::Success(length);
 }
-/// @brief Forms M/(beta*h²)+(1+alpha)*Kt in the unchanged full sparse pattern.
+/// @brief Forms M/(beta*h^2)+(1+alpha)*Kt in the unchanged full sparse pattern.
 Result<SparseMatrix> EffectiveTangent(const SparseMatrix& m,
                                       const PairedTangent& k,
                                       const DofManager& dofs, double h,
@@ -549,24 +553,6 @@ bool CorrectionPass(const std::array<HighLow, 4>& metrics) {
            Compare(x, HighLow(1e-10)) <= 0;
   });
 }
-Status SetRates(const SolidDynamicAcceptedFrameState& old,
-                const detail::SolidHhtPairedPredictor& predictor, double h,
-                const HhtParameters& p,
-                SolidDynamicAcceptedFrameState* candidate) {
-  auto rates = detail::EvaluateSolidHhtHighLowRates(
-      candidate->displacement, candidate->low.displacement, predictor,
-      old.acceleration, old.low.acceleration, h, p);
-  if (!rates.HasValue()) return rates.GetStatus();
-  candidate->velocity = std::move(rates.Value().velocity);
-  candidate->low.velocity = std::move(rates.Value().velocity_low);
-  candidate->acceleration = std::move(rates.Value().acceleration);
-  candidate->low.acceleration = std::move(rates.Value().acceleration_low);
-  candidate->algorithmic_acceleration =
-      std::move(rates.Value().algorithmic_acceleration);
-  candidate->low.algorithmic_acceleration =
-      std::move(rates.Value().algorithmic_acceleration_low);
-  return Status::Ok();
-}
 }  // namespace
 
 SolidHhtDynamicProcedureExecutor::SolidHhtDynamicProcedureExecutor(
@@ -600,6 +586,17 @@ Status SolidHhtDynamicProcedureExecutor::ExecuteInto(
 Status SolidHhtDynamicProcedureExecutor::ExecuteIntoForVerification(
     const Domain& domain, SolidDynamicAnalysisState& state,
     double alpha) const {
+  const detail::PairedSolidHhtIntegrator integrator;
+  NewtonStepAlgorithm algorithm;
+  return ExecuteSolidHhtCore(domain, state, alpha, parallel_for_, mass_solver_,
+                              tangent_solver_, integrator, algorithm);
+}
+
+Status ExecuteSolidHhtCore(
+    const Domain& domain, SolidDynamicAnalysisState& state, double alpha,
+    const ParallelFor& parallel_for, LinearSolver& mass_solver,
+    TangentSolver& tangent_solver, const detail::SolidHhtIntegrator& integrator,
+    EquilibriumAlgorithm& algorithm) {
   SolidDynamicIterationRecord record;
   auto fail = [&](const Status& failure) {
     record.stage = "failed";
@@ -630,7 +627,7 @@ Status SolidHhtDynamicProcedureExecutor::ExecuteIntoForVerification(
   auto mass_partition = partition.Partition(mass.Value(), dofs);
   if (!mass_partition.HasValue()) return fail(mass_partition.GetStatus());
   if (dofs.FreeDofCount() != 0) {
-    const auto status = mass_solver_.Factorize(mass_partition.Value().k_ff);
+    const auto status = mass_solver.Factorize(mass_partition.Value().k_ff);
     if (!status.IsOk()) return fail(status);
     environment = CheckArithmeticEnvironment(domain);
     if (!environment.IsOk()) return fail(environment);
@@ -655,7 +652,7 @@ Status SolidHhtDynamicProcedureExecutor::ExecuteIntoForVerification(
   if (!force.HasValue()) return fail(force.GetStatus());
   initial.external_force = std::move(force.Value());
   auto tangent =
-      EvaluateSolids(domain, solids.Value(), dofs, parallel_for_, &initial);
+      EvaluateSolids(domain, solids.Value(), dofs, parallel_for, &initial);
   if (!tangent.HasValue()) return fail(tangent.GetStatus());
   SolidDynamicIterationEvidence evidence;
   bool initial_converged = false;
@@ -682,7 +679,7 @@ Status SolidHhtDynamicProcedureExecutor::ExecuteIntoForVerification(
       const auto i = dofs.FreeDofs()[j];
       rhs[j] = Rounded(Negate(Pair(initial.residual, initial.low.residual, i)));
     }
-    status = mass_solver_.Solve(rhs, a);
+    status = mass_solver.Solve(rhs, a);
     if (!status.IsOk()) return fail(status);
     environment = CheckArithmeticEnvironment(domain);
     if (!environment.IsOk()) return fail(environment);
@@ -726,145 +723,188 @@ Status SolidHhtDynamicProcedureExecutor::ExecuteIntoForVerification(
     record = {};
     record.increment_index = increment;
     record.time = static_cast<double>(increment) * h;
-    auto predictor = detail::PredictSolidHhtHighLow(old, h, p);
-    if (!predictor.HasValue()) return fail(predictor.GetStatus());
-    auto candidate = old;
-    candidate.frame_index = candidate.increment_index = increment;
-    candidate.iteration_count = 0;
-    candidate.time = record.time;
-    candidate.is_initial = false;
-    candidate.iterations.clear();
-    // Begin from certified accepted geometry, not an unchecked predictor.
-    force = LoadAssembler::AssembleFullNodalLoad(model.Value(), dofs,
-                                                 candidate.time);
-    if (!force.HasValue()) return fail(force.GetStatus());
-    candidate.external_force = std::move(force.Value());
-    candidate.low.external_force = Vector(dofs.FullDofCount());
-    std::array<HighLow, 4> correction{}, fresh_correction{};
-    bool accepted = false;
-    for (std::uint32_t iteration = 0; iteration <= 100; ++iteration) {
-      record.stage = "evaluation";
-      record.outcome = "paired-candidate";
-      record.evidence = {};
-      record.evidence.iteration_index = iteration;
-      status = SetRates(old, predictor.Value(), h, p, &candidate);
-      if (!status.IsOk()) return fail(status);
-      tangent = EvaluateSolids(domain, solids.Value(), dofs, parallel_for_,
-                               &candidate);
-      if (!tangent.HasValue()) return fail(tangent.GetStatus());
-      status = RecoverEndpoint(domain, dofs, mass.Value(), &old, initial_energy,
-                               &candidate, &record.evidence);
-      if (!status.IsOk()) return fail(status);
-      auto MA = detail::MultiplySolidHhtMassHighLow(
-          mass.Value(), candidate.algorithmic_acceleration,
-          candidate.low.algorithmic_acceleration);
-      if (!MA.HasValue()) return fail(MA.GetStatus());
-      Vector rhs(dofs.FreeDofCount());
-      HighLow identity_metric, original_norm, solved_norm, old_norm;
-      for (std::size_t j = 0; j < dofs.FreeDofCount(); ++j) {
-        const auto i = dofs.FreeDofs()[j];
-        detail::SolidHhtPairedForceIdentity identity;
-        if (!detail::EvaluateSolidHhtHighLowForceIdentity(
-                mass.Value(), i, Pair(MA.Value().high, MA.Value().low, i),
-                candidate, old, p.alpha, &identity))
-          return fail(
-              Failure(domain, "solid-dynamic-nonfinite-residual",
-                      "Paired weighted force arithmetic is unsupported."));
-        rhs[j] = Rounded(Negate(identity.solved));
-        identity_metric = Maximum(identity_metric, identity.metric);
-        original_norm = Maximum(original_norm, Abs(identity.original));
-        solved_norm = Maximum(solved_norm, Abs(identity.solved));
-        old_norm =
-            Maximum(old_norm, Abs(Pair(old.residual, old.low.residual, i)));
-        if (i == record.evidence.worst_full_dof)
-          record.evidence.worst_weighted_terms = {
-              Rounded(identity.original), Rounded(identity.solved),
-              Rounded(Pair(old.residual, old.low.residual, i)),
-              Rounded(identity.scale)};
-      }
-      if (!Valid(identity_metric) || !Valid(original_norm) ||
-          !Valid(solved_norm) || !Valid(old_norm) ||
-          Compare(identity_metric, HighLow(1e-12)) > 0)
-        return fail(Failure(domain,
-                            "solid-dynamic-weighted-algebra-inconsistency",
-                            "Paired original and solved forces disagree beyond "
-                            "their uncancelled scale."));
-      record.evidence.weighted_equivalence_metric = Rounded(identity_metric);
-      record.evidence.weighted_residual_numerator = Rounded(original_norm);
-      record.evidence.recombined_residual_numerator = Rounded(solved_norm);
-      record.evidence.old_residual_numerator = Rounded(old_norm);
-      for (std::size_t c = 0; c < 4; ++c) {
-        if (!Valid(correction[c]) || !Valid(fresh_correction[c]))
-          return fail(detail::SolidHhtPairedKinematicsFailure());
-        record.evidence.correction_metrics[c] = Rounded(correction[c]);
-      }
-      record.evidence.correction_pass =
-          CorrectionPass(correction) && CorrectionPass(fresh_correction);
-      const auto update = CheckUpdates(old, candidate, p, h);
-      if (!Valid(update))
-        return fail(detail::SolidHhtPairedKinematicsFailure());
-      record.evidence.update_metric = Rounded(update);
-      record.evidence.update_pass = Compare(update, HighLow(1e-12)) <= 0;
-      candidate.iterations.push_back(record.evidence);
-      candidate.iteration_count = iteration;
-      if (record.evidence.residual_pass && record.evidence.correction_pass &&
-          record.evidence.update_pass) {
-        status = state.CommitAcceptedFrame(candidate);
-        if (!status.IsOk()) return fail(status);
-        record.stage = "accepted";
-        record.outcome = "increment";
-        state.RecordIteration(record);
-        accepted = true;
-        break;
-      }
-      state.RecordIteration(record);
-      if (iteration == 100)
-        return fail(Failure(
-            domain, "solid-dynamic-nonconvergence",
-            "Paired HHT endpoint did not converge in100 Newton solves."));
-      auto effective =
-          EffectiveTangent(mass.Value(), tangent.Value(), dofs, h, p);
-      if (!effective.HasValue()) return fail(effective.GetStatus());
-      auto reduced = partition.Partition(effective.Value(), dofs);
-      if (!reduced.HasValue()) return fail(reduced.GetStatus());
-      Vector du(dofs.FreeDofCount());
-      if (dofs.FreeDofCount() != 0) {
-        status = tangent_solver_.FactorizeFresh(reduced.Value().k_ff);
-        if (!status.IsOk()) return fail(status);
-        environment = CheckArithmeticEnvironment(domain);
-        if (!environment.IsOk()) return fail(environment);
-        status = tangent_solver_.SolveCorrection(rhs, du);
-        if (!status.IsOk()) return fail(status);
-        environment = CheckArithmeticEnvironment(domain);
-        if (!environment.IsOk()) return fail(environment);
-      }
-      if (du.Size() != dofs.FreeDofCount())
-        return fail(Failure(domain, "solid-dynamic-invalid-backend-result",
-                            "Tangent solve returned incompatible correction."));
-      for (std::size_t j = 0; j < du.Size(); ++j)
-        if (!std::isfinite(du[j]))
-          return fail(Failure(domain, "solid-dynamic-invalid-backend-result",
-                              "Tangent solve returned nonfinite correction."));
-      fresh_correction = FreshCorrectionMetrics(du, length.Value(), p);
-      const auto before = candidate;
-      for (std::size_t j = 0; j < du.Size(); ++j) {
-        const auto i = dofs.FreeDofs()[j];
-        const auto value =
-            Add(Pair(candidate.displacement, candidate.low.displacement, i),
-                HighLow(du[j] == 0 ? 0.0 : du[j]));
-        if (!Valid(value))
-          return fail(detail::SolidHhtPairedKinematicsFailure());
-        Store(value, &candidate.displacement, &candidate.low.displacement, i);
-      }
-      status = SetRates(old, predictor.Value(), h, p, &candidate);
-      if (!status.IsOk()) return fail(status);
-      correction =
-          ObservedCorrectionMetrics(before, candidate, h, length.Value());
-    }
-    if (!accepted)
-      return fail(Failure(domain, "solid-dynamic-nonconvergence",
-                          "No complete paired endpoint was accepted."));
+    status = detail::RunSolidHhtStep(
+        integrator, old, h, p, fail,
+        [&](const detail::SolidHhtIntegrator& step_integrator,
+            const detail::SolidHhtPairedPredictor& predictor)
+            -> Result<SolidDynamicAcceptedFrameState> {
+          auto candidate = old;
+          candidate.frame_index = candidate.increment_index = increment;
+          candidate.iteration_count = 0;
+          candidate.time = record.time;
+          candidate.is_initial = false;
+          candidate.iterations.clear();
+          // Begin from certified accepted geometry, not an unchecked predictor.
+          force = LoadAssembler::AssembleFullNodalLoad(model.Value(), dofs,
+                                                       candidate.time);
+          if (!force.HasValue())
+            return Result<SolidDynamicAcceptedFrameState>::Failure(fail(force.GetStatus()));
+          candidate.external_force = std::move(force.Value());
+          candidate.low.external_force = Vector(dofs.FullDofCount());
+          std::array<HighLow, 4> correction{}, fresh_correction{};
+          using StepResult = Result<std::optional<SolidDynamicAcceptedFrameState>>;
+          const auto report_failure = fail;
+          const auto record_iteration = [&](const auto& value) {
+            state.RecordIteration(value);
+          };
+          SolidHhtStep<SolidDynamicAcceptedFrameState> iteration_step(
+              [&](std::uint32_t iteration) -> StepResult {
+                const auto fail = [&](const Status& failure) {
+                  return StepResult::Failure(report_failure(failure));
+                };
+                record.stage = "evaluation";
+                record.outcome = "paired-candidate";
+                record.evidence = {};
+                record.evidence.iteration_index = iteration;
+                status =
+                    detail::SetSolidHhtRates(step_integrator, old, predictor, h, p, &candidate);
+                if (!status.IsOk())
+                  return fail(status);
+                tangent = EvaluateSolids(domain, solids.Value(), dofs, parallel_for,
+                                         &candidate);
+                if (!tangent.HasValue())
+                  return fail(tangent.GetStatus());
+                status =
+                    RecoverEndpoint(domain, dofs, mass.Value(), &old, initial_energy,
+                                    &candidate, &record.evidence);
+                if (!status.IsOk())
+                  return fail(status);
+                auto MA = detail::MultiplySolidHhtMassHighLow(
+                    mass.Value(), candidate.algorithmic_acceleration,
+                    candidate.low.algorithmic_acceleration);
+                if (!MA.HasValue())
+                  return fail(MA.GetStatus());
+                Vector rhs(dofs.FreeDofCount());
+                HighLow identity_metric, original_norm, solved_norm, old_norm;
+                for (std::size_t j = 0; j < dofs.FreeDofCount(); ++j) {
+                  const auto i = dofs.FreeDofs()[j];
+                  detail::SolidHhtPairedForceIdentity identity;
+                  if (!detail::EvaluateSolidHhtHighLowForceIdentity(
+                          mass.Value(), i, Pair(MA.Value().high, MA.Value().low, i),
+                          candidate, old, p.alpha, &identity))
+                    return fail(
+                        Failure(domain, "solid-dynamic-nonfinite-residual",
+                                "Paired weighted force arithmetic is unsupported."));
+                  rhs[j] = Rounded(Negate(identity.solved));
+                  identity_metric = Maximum(identity_metric, identity.metric);
+                  original_norm = Maximum(original_norm, Abs(identity.original));
+                  solved_norm = Maximum(solved_norm, Abs(identity.solved));
+                  old_norm =
+                      Maximum(old_norm, Abs(Pair(old.residual, old.low.residual, i)));
+                  if (i == record.evidence.worst_full_dof)
+                    record.evidence.worst_weighted_terms = {
+                        Rounded(identity.original), Rounded(identity.solved),
+                        Rounded(Pair(old.residual, old.low.residual, i)),
+                        Rounded(identity.scale)};
+                }
+                if (!Valid(identity_metric) || !Valid(original_norm) ||
+                    !Valid(solved_norm) || !Valid(old_norm) ||
+                    Compare(identity_metric, HighLow(1e-12)) > 0)
+                  return fail(
+                      Failure(domain, "solid-dynamic-weighted-algebra-inconsistency",
+                              "Paired original and solved forces disagree beyond "
+                              "their uncancelled scale."));
+                record.evidence.weighted_equivalence_metric =
+                    Rounded(identity_metric);
+                record.evidence.weighted_residual_numerator = Rounded(original_norm);
+                record.evidence.recombined_residual_numerator = Rounded(solved_norm);
+                record.evidence.old_residual_numerator = Rounded(old_norm);
+                for (std::size_t c = 0; c < 4; ++c) {
+                  if (!Valid(correction[c]) || !Valid(fresh_correction[c]))
+                    return fail(detail::SolidHhtPairedKinematicsFailure());
+                  record.evidence.correction_metrics[c] = Rounded(correction[c]);
+                }
+                record.evidence.correction_pass =
+                    CorrectionPass(correction) && CorrectionPass(fresh_correction);
+                const auto update = CheckUpdates(old, candidate, p, h);
+                if (!Valid(update))
+                  return fail(detail::SolidHhtPairedKinematicsFailure());
+                record.evidence.update_metric = Rounded(update);
+                record.evidence.update_pass = Compare(update, HighLow(1e-12)) <= 0;
+                candidate.iterations.push_back(record.evidence);
+                candidate.iteration_count = iteration;
+                if (record.evidence.residual_pass &&
+                    record.evidence.correction_pass && record.evidence.update_pass) {
+                  return StepResult::Success(candidate);
+                }
+                record_iteration(record);
+                if (iteration == 100)
+                  return fail(Failure(
+                      domain, "solid-dynamic-nonconvergence",
+                      "Paired HHT endpoint did not converge in100 Newton solves."));
+                auto effective =
+                    EffectiveTangent(mass.Value(), tangent.Value(), dofs, h, p);
+                if (!effective.HasValue())
+                  return fail(effective.GetStatus());
+                auto reduced = partition.Partition(effective.Value(), dofs);
+                if (!reduced.HasValue())
+                  return fail(reduced.GetStatus());
+                Vector du(dofs.FreeDofCount());
+                if (dofs.FreeDofCount() != 0) {
+                  status = tangent_solver.FactorizeFresh(reduced.Value().k_ff);
+                  if (!status.IsOk())
+                    return fail(status);
+                  environment = CheckArithmeticEnvironment(domain);
+                  if (!environment.IsOk())
+                    return fail(environment);
+                  status = tangent_solver.SolveCorrection(rhs, du);
+                  if (!status.IsOk())
+                    return fail(status);
+                  environment = CheckArithmeticEnvironment(domain);
+                  if (!environment.IsOk())
+                    return fail(environment);
+                }
+                if (du.Size() != dofs.FreeDofCount())
+                  return fail(
+                      Failure(domain, "solid-dynamic-invalid-backend-result",
+                              "Tangent solve returned incompatible correction."));
+                for (std::size_t j = 0; j < du.Size(); ++j)
+                  if (!std::isfinite(du[j]))
+                    return fail(
+                        Failure(domain, "solid-dynamic-invalid-backend-result",
+                                "Tangent solve returned nonfinite correction."));
+                fresh_correction = FreshCorrectionMetrics(du, length.Value(), p);
+                const auto before = candidate;
+                for (std::size_t j = 0; j < du.Size(); ++j) {
+                  const auto i = dofs.FreeDofs()[j];
+                  const auto value =
+                      Add(Pair(candidate.displacement, candidate.low.displacement, i),
+                          HighLow(du[j] == 0 ? 0.0 : du[j]));
+                  if (!Valid(value))
+                    return fail(detail::SolidHhtPairedKinematicsFailure());
+                  Store(value, &candidate.displacement, &candidate.low.displacement,
+                        i);
+                }
+                status =
+                    detail::SetSolidHhtRates(step_integrator, old, predictor, h, p, &candidate);
+                if (!status.IsOk())
+                  return fail(status);
+                correction =
+                    ObservedCorrectionMetrics(before, candidate, h, length.Value());
+                return StepResult::Success(std::nullopt);
+              },
+              100U);
+          const Status solved = iteration_step.Solve(algorithm);
+          if (!solved.IsOk())
+            return Result<SolidDynamicAcceptedFrameState>::Failure(solved);
+          if (!iteration_step.HasCandidate())
+            return Result<SolidDynamicAcceptedFrameState>::Failure(
+                fail(Failure(domain, "solid-dynamic-nonconvergence",
+                             "No complete paired endpoint was accepted.")));
+          return Result<SolidDynamicAcceptedFrameState>::Success(
+              iteration_step.TakeCandidate());
+        },
+        [&](SolidDynamicAcceptedFrameState&& accepted_candidate) -> Status {
+          status = state.CommitAcceptedFrame(accepted_candidate);
+          if (!status.IsOk())
+            return fail(status);
+          record.stage = "accepted";
+          record.outcome = "increment";
+          state.RecordIteration(record);
+          return Status::Ok();
+        });
+    if (!status.IsOk()) return status;
   }
   return Status::Ok();
 }
-}  // namespace fesa
+} // namespace fesa

src/fesa/analysis/solid_hht_integrator.h

@@ -0,0 +1,75 @@
+#ifndef FESA_ANALYSIS_SOLID_HHT_INTEGRATOR_H_
+#define FESA_ANALYSIS_SOLID_HHT_INTEGRATOR_H_
+
+#include <utility>
+#include "analysis/solid_hht_high_low.h"
+
+namespace fesa::detail {
+
+/// @brief Predicts and evaluates complete paired mechanical HHT kinematics.
+class SolidHhtIntegrator {
+ public:
+  virtual ~SolidHhtIntegrator() = default;
+  virtual Result<SolidHhtPairedPredictor> Predict(
+      const SolidDynamicAcceptedFrameState& old, double h,
+      const HhtParameters& parameters) const = 0;
+  virtual Result<SolidHhtPairedRates> EvaluateRates(
+      const Vector& high, const Vector& low,
+      const SolidHhtPairedPredictor& predictor, const Vector& old_acceleration,
+      const Vector& old_acceleration_low, double h,
+      const HhtParameters& parameters) const = 0;
+};
+
+/// @brief Retains every high/low physical and auxiliary acceleration channel.
+class PairedSolidHhtIntegrator final : public SolidHhtIntegrator {
+ public:
+  Result<SolidHhtPairedPredictor> Predict(
+      const SolidDynamicAcceptedFrameState& old, double h,
+      const HhtParameters& parameters) const override {
+    return PredictSolidHhtHighLow(old, h, parameters);
+  }
+  Result<SolidHhtPairedRates> EvaluateRates(
+      const Vector& high, const Vector& low,
+      const SolidHhtPairedPredictor& predictor, const Vector& old_acceleration,
+      const Vector& old_acceleration_low, double h,
+      const HhtParameters& parameters) const override {
+    return EvaluateSolidHhtHighLowRates(high, low, predictor, old_acceleration,
+                                        old_acceleration_low, h, parameters);
+  }
+};
+
+inline Status SetSolidHhtRates(const SolidHhtIntegrator& integrator,
+                const SolidDynamicAcceptedFrameState& old,
+                const SolidHhtPairedPredictor& predictor, double h,
+                const HhtParameters& p,
+                SolidDynamicAcceptedFrameState* candidate) {
+  auto rates = integrator.EvaluateRates(
+      candidate->displacement, candidate->low.displacement, predictor,
+      old.acceleration, old.low.acceleration, h, p);
+  if (!rates.HasValue()) return rates.GetStatus();
+  candidate->velocity = std::move(rates.Value().velocity);
+  candidate->low.velocity = std::move(rates.Value().velocity_low);
+  candidate->acceleration = std::move(rates.Value().acceleration);
+  candidate->low.acceleration = std::move(rates.Value().acceleration_low);
+  candidate->algorithmic_acceleration =
+      std::move(rates.Value().algorithmic_acceleration);
+  candidate->low.algorithmic_acceleration =
+      std::move(rates.Value().algorithmic_acceleration_low);
+  return Status::Ok();
+}
+/// @brief Preserves predictor failure recording, endpoint evaluation and commit.
+/// @note Borrowed callbacks do not escape; only commit may update history.
+template <typename Failure, typename Evaluate, typename Commit>
+Status RunSolidHhtStep(const SolidHhtIntegrator& integrator,
+                       const SolidDynamicAcceptedFrameState& old, double h,
+                       const HhtParameters& parameters, Failure&& failure,
+                       Evaluate&& evaluate, Commit&& commit) {
+  auto predictor = integrator.Predict(old, h, parameters);
+  if (!predictor.HasValue()) return failure(predictor.GetStatus());
+  auto pending = evaluate(integrator, predictor.Value());
+  if (!pending.HasValue()) return pending.GetStatus();
+  return commit(std::move(pending.Value()));
+}
+
+}  // namespace fesa::detail
+#endif  // FESA_ANALYSIS_SOLID_HHT_INTEGRATOR_H_

src/fesa/analysis/solid_static_core.h

@@ -0,0 +1,27 @@
+#ifndef FESA_ANALYSIS_SOLID_STATIC_CORE_H_
+#define FESA_ANALYSIS_SOLID_STATIC_CORE_H_
+#include "fesa/core/status.h"
+namespace fesa {
+class Domain;
+class SolidStaticState;
+class ParallelFor;
+class LinearSolver;
+class TangentSolver;
+class EquilibriumAlgorithm;
+/// @brief Borrows the production static core's execution/solve/iteration policy.
+/// @note Every adapter must outlive ExecuteInto; state owns accepted history.
+class SolidStaticCore {
+ public:
+  SolidStaticCore(const ParallelFor& parallel_for, LinearSolver& linear_solver,
+                  TangentSolver& tangent_solver, EquilibriumAlgorithm& algorithm)
+      : parallel_for_(parallel_for), linear_solver_(linear_solver),
+        tangent_solver_(tangent_solver), algorithm_(algorithm) {}
+  Status ExecuteInto(const Domain& domain, SolidStaticState& state) const;
+ private:
+  const ParallelFor& parallel_for_;
+  LinearSolver& linear_solver_;
+  TangentSolver& tangent_solver_;
+  EquilibriumAlgorithm& algorithm_;
+};
+}  // namespace fesa
+#endif  // FESA_ANALYSIS_SOLID_STATIC_CORE_H_

src/fesa/analysis/solid_static_procedure.cpp

@@ -1,5 +1,8 @@
 #include "fesa/analysis/solid_static_procedure.h"
 
+#include "equilibrium_algorithm.h"
+#include "analysis/solid_static_core.h"
+
 #include <algorithm>
 #include <array>
 #include <cmath>
@@ -21,6 +24,8 @@
 #include "fesa/solvers/linear/linear_solver.h"
 #include "fesa/solvers/linear/tangent_solver.h"
 
+#include "assembly/ordered_contribution_internal.h"
+
 namespace fesa {
 namespace {
 constexpr std::uint32_t kMaximumIterations = 100U;
@@ -28,7 +33,7 @@ constexpr double kRoundoffBudget =
     512.0 * std::numeric_limits<double>::epsilon();
 
 struct RuntimeSolid {
-  const Hex8Element* element;
+  std::unique_ptr<SolidTrialElement> element;
   std::vector<std::size_t> scatter;
 };
 struct SolidAssembly {
@@ -131,9 +136,8 @@ Result<SolidAssembly> Assemble(const std::vector<RuntimeSolid>& solids,
     const auto& response = responses[e]->Value();
     for (std::size_t i = 0U; i < 24U; ++i) {
       force[solids[e].scatter[i]] += response.internal_force[i];
-      for (std::size_t j = 0U; j < 24U; ++j)
-        contributions.push_back({solids[e].scatter[i], solids[e].scatter[j],
-                                 response.tangent(i, j), e, 24U * i + j});
+      assembly_internal::AppendLocalMatrixRow(
+          response.tangent, solids[e].scatter, i, e, contributions);
     }
     energy += response.strain_energy;
     points.insert(points.end(), response.points.begin(), response.points.end());
@@ -283,6 +287,13 @@ SolidStaticProcedureExecutor::SolidStaticProcedureExecutor(
 
 Status SolidStaticProcedureExecutor::ExecuteInto(
     const Domain& domain, SolidStaticState& state) const {
+  NewtonStepAlgorithm algorithm;
+  return SolidStaticCore(parallel_for_, linear_solver_, tangent_solver_, algorithm)
+      .ExecuteInto(domain, state);
+}
+
+Status SolidStaticCore::ExecuteInto(
+    const Domain& domain, SolidStaticState& state) const {
   if (state.initialized_)
     return Failure(domain, "solid-static-observer-not-fresh",
                    "Execution requires a fresh static observer.");
@@ -309,14 +320,14 @@ Status SolidStaticProcedureExecutor::ExecuteInto(
   state = std::move(baseline.Value());
   std::vector<RuntimeSolid> solids;
   for (const auto& element : elements) {
-    const auto* hex = dynamic_cast<const Hex8Element*>(element.get());
+    auto hex = ElementFactory{}.BindSolidTrial(*element);
     if (hex == nullptr)
       return Failure(domain, "invalid-solid-static-element",
                      "Solid STATIC requires full-integration Hex8 kernels.",
                      FailureCategory::kModel);
     auto scatter = dofs.ElementScatter(hex->DofLayout());
     if (!scatter.HasValue()) return scatter.GetStatus();
-    solids.push_back({hex, std::move(scatter.Value())});
+    solids.push_back({std::move(hex), std::move(scatter.Value())});
   }
   auto stiffness = SparseAssembler::Assemble(view, dofs, parallel_for_);
   if (!stiffness.HasValue()) return stiffness.GetStatus();
@@ -336,7 +347,7 @@ Status SolidStaticProcedureExecutor::ExecuteInto(
     // Preserve the required factorization-before-load-assembly lifecycle.
     auto load = LoadAssembler::AssembleFullNodalLoad(model.Value(), dofs);
     if (!load.HasValue()) return load.GetStatus();
-    auto rhs = LoadAssembler::EffectiveFreeRhs(
+    auto rhs = constraints.EffectiveFreeRhs(
         load.Value(), partition.Value().k_fc, dofs.PrescribedValues(), dofs);
     if (!rhs.HasValue()) return rhs.GetStatus();
     Vector free{dofs.FreeDofCount()};
@@ -369,91 +380,128 @@ Status SolidStaticProcedureExecutor::ExecuteInto(
     for (std::size_t c = 0U; c < dofs.ConstrainedDofCount(); ++c)
       trial[dofs.ConstrainedDofs()[c]] =
           increment.load_factor * dofs.PrescribedValues()[c];
-    for (std::uint32_t iteration = 1U; iteration <= kMaximumIterations;
-         ++iteration) {
+    struct SolidStepCandidate {
+      SolidStaticFrame frame;
       SolidStaticIterationRecord record;
-      record.increment_index = increment.increment_index;
-      record.load_factor = increment.load_factor;
-      record.iteration = iteration;
-      record.stage = "entered";
-      const auto fail = [&](const Status& failure) {
-        record.diagnostic_code = failure.Diagnostics().empty()
-                                     ? "solid-static-failure"
-                                     : failure.Diagnostics()[0].code;
-        record.failure_reason = failure.Diagnostics().empty()
-                                    ? "Static trial failed."
-                                    : failure.Diagnostics()[0].message;
-        state.iterations_.push_back(record);
-        return failure;
-      };
-      record.stage = "trial-recovery";
-      auto assembly = Assemble(solids, dofs, trial, true, parallel_for_);
-      if (!assembly.HasValue()) return fail(assembly.GetStatus());
-      SolidStaticFrame frame = state.committed_;
-      frame.balance = {};
-      frame.global_equilibrium = {};
-      frame.frame_index =
-          static_cast<std::uint32_t>(state.accepted_frames_.size());
-      frame.increment_index = increment.increment_index;
-      frame.load_factor = increment.load_factor;
-      frame.iteration_count = iteration;
-      frame.is_factor_one = increment.is_factor_one;
-      frame.displacement = trial;
-      frame.internal_force = std::move(assembly.Value().force);
-      frame.external_force = base_load.Value();
-      frame.external_force.Scale(increment.load_factor);
-      frame.solid_results = std::move(assembly.Value().points);
-      frame.physical_strain_energy = assembly.Value().energy;
-      auto status = CompleteFrame(domain, dofs, true, stiffness.Value(), frame);
-      if (!status.IsOk()) return fail(status);
-      record.stage = "tangent-partition";
-      auto partition = constraints.Partition(assembly.Value().tangent, dofs);
-      if (!partition.HasValue()) return fail(partition.GetStatus());
-      Vector correction{dofs.FreeDofCount()};
-      // Empty free is vacuous; prescribed geometry/recovery above still runs.
-      if (dofs.FreeDofCount() != 0U) {
-        record.stage = "tangent-factorization";
-        status = tangent_solver_.FactorizeFresh(partition.Value().k_ff);
-        if (!status.IsOk()) return fail(status);
-        auto rhs = constraints.GatherFree(frame.residual, dofs);
-        rhs.Scale(-1.0);
-        record.stage = "correction-solve";
-        status = tangent_solver_.SolveCorrection(rhs, correction);
-        if (!status.IsOk()) return fail(status);
-      }
-      Vector current_increment{dofs.FreeDofCount()};
-      for (std::size_t f = 0U; f < dofs.FreeDofCount(); ++f) {
-        const auto full = dofs.FreeDofs()[f];
-        current_increment[f] = trial[full] - start[full];
-      }
-      record.stage = "convergence";
-      auto convergence = EvaluateSolidStaticConvergence(
-          constraints.GatherFree(frame.residual, dofs),
-          constraints.GatherFree(frame.internal_force, dofs),
-          constraints.GatherFree(frame.external_force, dofs), correction,
-          current_increment);
-      if (!convergence.HasValue()) return fail(convergence.GetStatus());
-      record.force_residual = convergence.Value().force_residual;
-      record.translation_correction =
-          convergence.Value().translation_correction;
-      record.convergence_evaluated = true;
-      if (record.force_residual.passed &&
-          record.translation_correction.passed) {
-        record.stage = "commit";
-        status = state.CommitAcceptedFrame(frame);
-        if (!status.IsOk()) return fail(status);
-        record.accepted = true;
-        state.iterations_.push_back(record);
-        break;
-      }
-      if (iteration == kMaximumIterations)
-        return fail(Failure(domain, "solid-static-nonconvergence",
-                            "Solid STATIC exceeded 100 Newton iterations."));
-      for (std::size_t f = 0U; f < dofs.FreeDofCount(); ++f)
-        trial[dofs.FreeDofs()[f]] += correction[f];
-      record.stage = "continue";
-      state.iterations_.push_back(record);
+    };
+    const auto observe_iteration =
+        [&](const SolidStaticIterationRecord& record) {
+          state.iterations_.push_back(record);
+        };
+    SolidFullNewtonStep<SolidStepCandidate> iteration_step(
+        [&](std::uint32_t iteration)
+            -> Result<std::optional<SolidStepCandidate>> {
+          SolidStaticIterationRecord record;
+          record.increment_index = increment.increment_index;
+          record.load_factor = increment.load_factor;
+          record.iteration = iteration;
+          record.stage = "entered";
+          const auto fail = [&](const Status& failure) {
+            record.diagnostic_code = failure.Diagnostics().empty()
+                                         ? "solid-static-failure"
+                                         : failure.Diagnostics()[0].code;
+            record.failure_reason = failure.Diagnostics().empty()
+                                        ? "Static trial failed."
+                                        : failure.Diagnostics()[0].message;
+            observe_iteration(record);
+            return Result<std::optional<SolidStepCandidate>>::Failure(failure);
+          };
+          record.stage = "trial-recovery";
+          auto assembly = Assemble(solids, dofs, trial, true, parallel_for_);
+          if (!assembly.HasValue())
+            return fail(assembly.GetStatus());
+          SolidStaticFrame frame = state.committed_;
+          frame.balance = {};
+          frame.global_equilibrium = {};
+          frame.frame_index =
+              static_cast<std::uint32_t>(state.accepted_frames_.size());
+          frame.increment_index = increment.increment_index;
+          frame.load_factor = increment.load_factor;
+          frame.iteration_count = iteration;
+          frame.is_factor_one = increment.is_factor_one;
+          frame.displacement = trial;
+          frame.internal_force = std::move(assembly.Value().force);
+          frame.external_force = base_load.Value();
+          frame.external_force.Scale(increment.load_factor);
+          frame.solid_results = std::move(assembly.Value().points);
+          frame.physical_strain_energy = assembly.Value().energy;
+          auto status =
+              CompleteFrame(domain, dofs, true, stiffness.Value(), frame);
+          if (!status.IsOk())
+            return fail(status);
+          record.stage = "tangent-partition";
+          auto partition =
+              constraints.Partition(assembly.Value().tangent, dofs);
+          if (!partition.HasValue())
+            return fail(partition.GetStatus());
+          Vector correction{dofs.FreeDofCount()};
+          // Empty free is vacuous; prescribed geometry/recovery above still
+          // runs.
+          if (dofs.FreeDofCount() != 0U) {
+            record.stage = "tangent-factorization";
+            status = tangent_solver_.FactorizeFresh(partition.Value().k_ff);
+            if (!status.IsOk())
+              return fail(status);
+            auto rhs = constraints.GatherFree(frame.residual, dofs);
+            rhs.Scale(-1.0);
+            record.stage = "correction-solve";
+            status = tangent_solver_.SolveCorrection(rhs, correction);
+            if (!status.IsOk())
+              return fail(status);
+          }
+          Vector current_increment{dofs.FreeDofCount()};
+          for (std::size_t f = 0U; f < dofs.FreeDofCount(); ++f) {
+            const auto full = dofs.FreeDofs()[f];
+            current_increment[f] = trial[full] - start[full];
+          }
+          record.stage = "convergence";
+          auto convergence = EvaluateSolidStaticConvergence(
+              constraints.GatherFree(frame.residual, dofs),
+              constraints.GatherFree(frame.internal_force, dofs),
+              constraints.GatherFree(frame.external_force, dofs), correction,
+              current_increment);
+          if (!convergence.HasValue())
+            return fail(convergence.GetStatus());
+          record.force_residual = convergence.Value().force_residual;
+          record.translation_correction =
+              convergence.Value().translation_correction;
+          record.convergence_evaluated = true;
+          if (record.force_residual.passed &&
+              record.translation_correction.passed) {
+            record.stage = "commit";
+            return Result<std::optional<SolidStepCandidate>>::Success(
+                SolidStepCandidate{std::move(frame), record});
+          }
+          if (iteration == kMaximumIterations)
+            return fail(
+                Failure(domain, "solid-static-nonconvergence",
+                        "Solid STATIC exceeded 100 Newton iterations."));
+          for (std::size_t f = 0U; f < dofs.FreeDofCount(); ++f)
+            trial[dofs.FreeDofs()[f]] += correction[f];
+          record.stage = "continue";
+          observe_iteration(record);
+          return Result<std::optional<SolidStepCandidate>>::Success(
+              std::nullopt);
+        },
+        kMaximumIterations);
+    const Status solved = iteration_step.Solve(algorithm_);
+    if (!solved.IsOk())
+      return solved;
+    auto candidate = iteration_step.TakeCandidate();
+    auto& record = candidate.record;
+    const Status committed = state.CommitAcceptedFrame(candidate.frame);
+    if (!committed.IsOk()) {
+      record.diagnostic_code = committed.Diagnostics().empty()
+                                   ? "solid-static-failure"
+                                   : committed.Diagnostics()[0].code;
+      record.failure_reason = committed.Diagnostics().empty()
+                                  ? "Static trial failed."
+                                  : committed.Diagnostics()[0].message;
+      observe_iteration(record);
+      return committed;
     }
+    record.accepted = true;
+    observe_iteration(record);
   }
   return Status::Ok();
 }

src/fesa/analysis/solid_static_state.cpp

@@ -37,10 +37,9 @@ double InfinityNorm(const Vector& values) {
   return norm;
 }
 /// @brief Compares immutable semantic and raw source identities.
-bool SameIdentity(const SourceEntityId& a, const SourceEntityId& b) {
-  return a.instance_name == b.instance_name &&
-         a.source_label == b.source_label &&
-         a.source_label_text == b.source_label_text;
+bool SameIdentity(const SourceEntityId& a,
+                        const SourceEntityId& b) {
+  return fesa::SourceIdentityEquals(a, b);
 }
 /// @brief Builds one raw criterion with the approved branch and physical unit.
 NewtonChannelDecision Decision(const char* name, double numerator,
@@ -119,7 +118,7 @@ Result<SolidStaticState> SolidStaticState::Create(const Domain& domain,
     auto element = ElementFactory{}.Create(domain.Elements()[e], domain);
     if (!element.HasValue())
       return Result<SolidStaticState>::Failure(element.GetStatus());
-    const auto* hex = dynamic_cast<const Hex8Element*>(element.Value().get());
+    auto hex = ElementFactory{}.BindSolidTrial(*element.Value());
     if (hex == nullptr)
       return Result<SolidStaticState>::Failure(StateFailure(
           "invalid-solid-static-state", "Static state requires Hex8 kernels."));

src/fesa/analysis/thermal_analysis_state.cpp

@@ -8,6 +8,9 @@
 #include <utility>
 #include <vector>
 
+#include "fesa/assembly/thermal_assembler.h"
+#include "math/finite_values.h"
+
 namespace fesa {
 namespace {
 
@@ -23,9 +26,7 @@ Status Failure(const std::string& message) {
 
 /// @brief Checks every stored scalar without imposing a temperature sign bound.
 bool Finite(const Vector& vector) {
-  for (std::size_t i = 0; i < vector.Size(); ++i)
-    if (!std::isfinite(vector[i])) return false;
-  return true;
+  return math_internal::IsFinite(vector);
 }
 
 /// @brief Compares prescribed row identities without conflating node and row
@@ -64,8 +65,8 @@ Result<ThermalAnalysisState> ThermalAnalysisState::Create(
   for (const auto node : state.node_order_)
     state.node_source_ids_.push_back(domain.Nodes()[node].source_id);
   for (std::size_t index = 0; index < state.element_order_.size(); ++index) {
-    state.element_source_ids_.push_back(assembly.Kernels()[index].SourceId());
-    const auto frame = assembly.Kernels()[index].Recover({});
+    state.element_source_ids_.push_back(assembly.Elements()[index]->DofLayout().source_id);
+    const auto frame = assembly.Elements()[index]->Recover({});
     if (!frame.HasValue())
       return Result<ThermalAnalysisState>::Failure(frame.GetStatus());
     state.local_frames_.push_back(frame.Value().frames);

src/fesa/analysis/thermal_transient_algebra.cpp

@@ -7,8 +7,10 @@
 #include <string>
 #include <utility>
 
+#include "fesa/assembly/thermal_assembler.h"
 #include "thermal_transient_bounds.h"
 #include "math/dense_blas_internal.h"
+#include "math/finite_values.h"
 
 namespace fesa::thermal_transient_internal {
 namespace {
@@ -35,9 +37,7 @@ Status Failure(const std::string& message) {
 }
 /// @brief Checks every scalar while preserving signed temperatures and powers.
 bool Finite(const Vector& vector) {
-  for (std::size_t i = 0; i < vector.Size(); ++i)
-    if (!std::isfinite(vector[i])) return false;
-  return true;
+  return math_internal::IsFinite(vector);
 }
 /// @brief Checks aligned full operators and their coefficient-error storage.
 bool SamePattern(const SparseMatrix& a, const SparseMatrix& b) {
@@ -500,6 +500,16 @@ Status RunThermalHistory(const ThermalAssembly& assembly,
                          const DofManager& dofs, ThermalAnalysisState& state,
                          LinearSolver& solver, const ThermalRecovery& recovery,
                          std::vector<ThermalStepEvidence>* evidence) {
+  const BackwardEulerHeatIntegrator integrator;
+  return RunThermalHistory(assembly, dofs, state, solver, integrator, recovery,
+                            evidence);
+}
+
+Status RunThermalHistory(const ThermalAssembly& assembly,
+                         const DofManager& dofs, ThermalAnalysisState& state,
+                         LinearSolver& solver, const HeatStepIntegrator& integrator,
+                         const ThermalRecovery& recovery,
+                         std::vector<ThermalStepEvidence>* evidence) {
   if (!dofs.ValidateInvariants().IsOk() ||
       dofs.Profile() != DofProfile::kThermal ||
       dofs.FullDofCount() != state.CommittedState().temperature.Size() ||
@@ -517,19 +527,21 @@ Status RunThermalHistory(const ThermalAssembly& assembly,
        i <= count; ++i) {
     const auto frame = state.TimeGrid().Frame(static_cast<std::uint32_t>(i));
     if (!frame.HasValue()) return frame.GetStatus();
-    auto candidate = SolveThermalIncrement(system, partition,
-                                           state.CommittedState().temperature,
-                                           frame.Value().delta, solver, cache);
-    if (!candidate.HasValue()) return candidate.GetStatus();
-    auto flux = recovery(candidate.Value().temperature);
-    if (!flux.HasValue()) return flux.GetStatus();
-    auto completed = state.MakeCompletedFrame(
-        static_cast<std::uint32_t>(i), std::move(candidate.Value().temperature),
-        std::move(candidate.Value().reaction), std::move(flux.Value()));
-    if (!completed.HasValue()) return completed.GetStatus();
-    const auto committed = state.CommitAcceptedFrame(completed.Value());
-    if (!committed.IsOk()) return committed;
-    if (evidence) evidence->push_back(candidate.Value().evidence);
+    const Status step_status = RunThermalStep(
+        integrator, system, partition, state.CommittedState().temperature,
+        frame.Value().delta, solver, cache, recovery,
+        [&](ThermalStepCandidate&& candidate,
+            std::vector<ThermalElementFlux>&& flux) -> Status {
+          auto completed = state.MakeCompletedFrame(
+              static_cast<std::uint32_t>(i), std::move(candidate.temperature),
+              std::move(candidate.reaction), std::move(flux));
+          if (!completed.HasValue()) return completed.GetStatus();
+          const auto committed = state.CommitAcceptedFrame(completed.Value());
+          if (!committed.IsOk()) return committed;
+          if (evidence) evidence->push_back(candidate.evidence);
+          return Status::Ok();
+        });
+    if (!step_status.IsOk()) return step_status;
   }
   return Status::Ok();
 }

src/fesa/analysis/thermal_transient_algebra.h

@@ -4,8 +4,10 @@
 #include <functional>
 #include <optional>
 #include <vector>
+#include <utility>
 
 #include "fesa/analysis/thermal_analysis_state.h"
+#include "fesa/math/sparse_matrix.h"
 #include "fesa/solvers/linear/linear_solver.h"
 
 namespace fesa::thermal_transient_internal {
@@ -84,11 +86,52 @@ Result<ThermalStepCandidate> SolveThermalIncrement(
     const Vector& old_temperature, double delta, LinearSolver& solver,
     ThermalFactorization& factorization);
 
+/// @brief Solves one thermal increment without committing accepted history.
+class HeatStepIntegrator {
+public:
+  virtual ~HeatStepIntegrator() = default;
+  virtual Result<ThermalStepCandidate>
+  SolveIncrement(const ThermalSystem &system, const ThermalPartition &partition,
+                 const Vector &old_temperature, double delta,
+                 LinearSolver &solver,
+                 ThermalFactorization &factorization) const = 0;
+};
+
+/// @brief Preserves backward Euler actual-delta and factorization reuse policy.
+class BackwardEulerHeatIntegrator final : public HeatStepIntegrator {
+public:
+  Result<ThermalStepCandidate>
+  SolveIncrement(const ThermalSystem &system, const ThermalPartition &partition,
+                 const Vector &old_temperature, double delta,
+                 LinearSolver &solver,
+                 ThermalFactorization &factorization) const override {
+    return SolveThermalIncrement(system, partition, old_temperature, delta,
+                                 solver, factorization);
+  }
+};
+
 /// @brief Provides an internal recovery seam for the actual history commit
 /// path.
 using ThermalRecovery = std::function<Result<std::vector<ThermalElementFlux>>(
     const Vector& temperature)>;
 
+/// @brief Runs the actual solve/recovery/commit sequence without owning history.
+/// @note Commit receives a validated unpublished candidate only after recovery.
+template <typename Commit>
+Status RunThermalStep(const HeatStepIntegrator& integrator,
+                      const ThermalSystem& system,
+                      const ThermalPartition& partition,
+                      const Vector& old_temperature, double delta,
+                      LinearSolver& solver, ThermalFactorization& factorization,
+                      const ThermalRecovery& recovery, Commit&& commit) {
+  auto candidate = integrator.SolveIncrement(system, partition, old_temperature,
+                                            delta, solver, factorization);
+  if (!candidate.HasValue()) return candidate.GetStatus();
+  auto flux = recovery(candidate.Value().temperature);
+  if (!flux.HasValue()) return flux.GetStatus();
+  return commit(std::move(candidate.Value()), std::move(flux.Value()));
+}
+
 /// @brief Advances an existing raw/accepted history, preserving it on every
 /// failure.
 /// @note Recovery runs after algebra validation and before atomic commit.
@@ -101,5 +144,13 @@ Status RunThermalHistory(const ThermalAssembly& assembly,
                          LinearSolver& solver, const ThermalRecovery& recovery,
                          std::vector<ThermalStepEvidence>* evidence = nullptr);
 
+/// @brief Borrows a caller-selected integrator for the complete history core.
+/// @note Integrator and other referenced adapters outlive the synchronous call.
+Status RunThermalHistory(const ThermalAssembly& assembly,
+                         const DofManager& dofs, ThermalAnalysisState& state,
+                         LinearSolver& solver, const HeatStepIntegrator& integrator,
+                         const ThermalRecovery& recovery,
+                         std::vector<ThermalStepEvidence>* evidence = nullptr);
+
 }  // namespace fesa::thermal_transient_internal
 #endif  // FESA_ANALYSIS_THERMAL_TRANSIENT_ALGEBRA_H_

src/fesa/analysis/transient_heat_procedure.cpp

@@ -1,6 +1,7 @@
 #include "fesa/analysis/transient_heat_procedure.h"
 
 #include <utility>
+#include "fesa/assembly/thermal_assembler.h"
 
 #include "thermal_transient_algebra.h"
 

src/fesa/app/fesa_application.cpp

@@ -12,6 +12,9 @@
 #include "fesa/analysis/nonlinear_static_procedure.h"
 #include "fesa/analysis/prepared_analysis.h"
 #include "fesa/analysis/solid_frequency_procedure.h"
+#include "fesa/analysis/solid_hht_dynamic_procedure.h"
+#include "fesa/analysis/solid_static_procedure.h"
+#include "fesa/analysis/transient_heat_procedure.h"
 #include "fesa/app/output_paths.h"
 #include "fesa/assembly/parallel_for.h"
 #include "fesa/core/diagnostic.h"
@@ -21,6 +24,7 @@
 #include "fesa/io/hdf5/nonlinear_hdf5_results_writer.h"
 #include "fesa/io/hdf5/solid_hdf5_results_writer.h"
 #include "fesa/io/hdf5/thermal_hdf5_results_writer.h"
+#include "fesa/solvers/eigen/mkl_feast_eigen_solver.h"
 #include "fesa/solvers/linear/mkl_pardiso_solver.h"
 #include "fesa/solvers/linear/mkl_pardiso_tangent_solver.h"
 
@@ -84,6 +88,7 @@ int FesaApplication::Run(const std::vector<std::string>& arguments) {
   }
 
   TbbParallelFor parallel_for;
+  const MklFeastEigenSolver eigen_solver;
   MklPardisoSolver linear_solver;
   MklPardisoTangentSolver tangent_solver;
   Hdf5ResultsWriter linear_writer;
@@ -105,23 +110,12 @@ int FesaApplication::Run(const std::vector<std::string>& arguments) {
   if (!prepared.HasValue()) {
     status = prepared.GetStatus();
   } else {
-    LinearStaticProcedureExecutor linear_executor(parallel_for, linear_solver);
-    NonlinearStaticProcedureExecutor nonlinear_executor(parallel_for,
-                                                        tangent_solver);
-    const LinearFrequencyProcedureExecutor frequency_executor;
-    const HhtDynamicProcedureExecutor dynamic_executor(
-        parallel_for, linear_solver, tangent_solver);
-    const TransientHeatProcedureExecutor thermal_executor(parallel_for,
-                                                          linear_solver);
-    const SolidStaticProcedureExecutor solid_static(parallel_for, linear_solver,
-                                                    tangent_solver);
-    const SolidFrequencyProcedureExecutor solid_frequency;
-    const SolidHhtDynamicProcedureExecutor solid_dynamic(
-        parallel_for, linear_solver, tangent_solver);
-    Result<PreparedAnalysisOutcome> outcome = ExecutePreparedAnalysis(
-        prepared.Value().domain, linear_executor, nonlinear_executor,
-        frequency_executor, log, &dynamic_executor, &thermal_executor,
-        &solid_static, &solid_frequency, &solid_dynamic);
+    auto procedure = CreateAnalysisProcedure(
+        prepared.Value().domain, parallel_for, linear_solver, tangent_solver,
+        eigen_solver, log);
+    Result<PreparedAnalysisOutcome> outcome = procedure.HasValue()
+        ? ExecutePreparedAnalysis(prepared.Value().domain, *procedure.Value())
+        : Result<PreparedAnalysisOutcome>::Failure(procedure.GetStatus());
     if (!outcome.HasValue()) {
       status = outcome.GetStatus();
     } else {

src/fesa/assembly/load_assembler.cpp

@@ -11,7 +11,8 @@
 #include "fesa/constraints/essential_constraint_policy.h"
 #include "fesa/loads/load.h"
 #include "fesa/model/source_target_resolver.h"
-#include "math/dense_blas_internal.h"
+
+#include "assembly/ordered_contribution_internal.h"
 
 namespace fesa {
 namespace {
@@ -27,20 +28,6 @@ Status LoadFailure(const std::string& code, const SourceLocation& location,
       {{Severity::kError, code, location, keyword, identity, message}});
 }
 
-Status ValidateFiniteVector(const Vector& values,
-                            const SourceLocation& location,
-                            const std::string& identity) {
-  for (std::size_t index = 0U; index < values.Size(); ++index) {
-    if (!std::isfinite(values[index])) {
-      return LoadFailure("nonfinite-load-value", location, "LOAD_ASSEMBLER",
-                         identity + ":" + std::to_string(index),
-                         "Load and prescribed displacement vectors must "
-                         "contain finite values.");
-    }
-  }
-  return Status::Ok();
-}
-
 Status ValidateShellMoments(const Domain& domain, const Vector& full_load) {
   if (domain.ShellElements().Empty()) {
     return Status::Ok();
@@ -224,14 +211,13 @@ Result<Vector> LoadAssembler::AssembleFullNodalLoad(const AnalysisModel& model,
   for (const auto& contributions : contributions_by_load) {
     for (const auto& contribution : contributions) {
       const std::size_t full_dof = contribution.full_dof_index;
-      const double accumulated = full_load[full_dof] + contribution.value;
-      if (!std::isfinite(accumulated)) {
+      if (!assembly_internal::AccumulateFiniteLoad(
+              full_load, full_dof, contribution.value)) {
         return Result<Vector>::Failure(LoadFailure(
             "nonfinite-load-accumulation", model.Step().Location(),
             "LOAD_ASSEMBLER", std::to_string(full_dof),
             "Source-order load accumulation produced a nonfinite value."));
       }
-      full_load[full_dof] = accumulated;
     }
   }
   const Status shell_moment_status = ValidateShellMoments(domain, full_load);
@@ -245,101 +231,8 @@ Result<Vector> LoadAssembler::EffectiveFreeRhs(const Vector& full_load,
                                                const SparseMatrix& kfc,
                                                const Vector& prescribed_values,
                                                const DofManager& dofs) {
-  const SourceLocation location{{}, 0U};
-  if (dofs.FullDofCount() != full_load.Size()) {
-    return Result<Vector>::Failure(
-        LoadFailure("invalid-load-dimensions", location, "LOAD_ASSEMBLER",
-                    std::to_string(dofs.FullDofCount()),
-                    "The DofManager full dimension must match the full load."));
-  }
-  const Status dof_status = dofs.ValidateInvariants();
-  if (!dof_status.IsOk()) {
-    return Result<Vector>::Failure(dof_status);
-  }
-  if (kfc.Rows() != dofs.FreeDofCount() ||
-      kfc.Columns() != dofs.ConstrainedDofCount() ||
-      prescribed_values.Size() != dofs.ConstrainedDofCount()) {
-    return Result<Vector>::Failure(LoadFailure(
-        "invalid-load-dimensions", location, "LOAD_ASSEMBLER",
-        std::to_string(kfc.Rows()) + "x" + std::to_string(kfc.Columns()),
-        "Kfc rows/columns and prescribed values must match free/constrained "
-        "order."));
-  }
-  const Status matrix_status = kfc.Validate();
-  if (!matrix_status.IsOk()) {
-    return Result<Vector>::Failure(matrix_status);
-  }
-  const Status load_status =
-      ValidateFiniteVector(full_load, location, "full-load");
-  if (!load_status.IsOk()) {
-    return Result<Vector>::Failure(load_status);
-  }
-  const Status prescribed_status =
-      ValidateFiniteVector(prescribed_values, location, "prescribed-values");
-  if (!prescribed_status.IsOk()) {
-    return Result<Vector>::Failure(prescribed_status);
-  }
-
-  Vector entry_coefficients{kfc.Values().size()};
-  Vector entry_prescribed{kfc.Values().size()};
-  for (std::size_t position = 0U; position < kfc.Values().size(); ++position) {
-    entry_coefficients[position] = kfc.Values()[position];
-    entry_prescribed[position] =
-        prescribed_values[kfc.ColumnIndices()[position]];
-  }
-  Vector entry_products{0U};
-  try {
-    entry_products = dense_blas_internal::MultiplyDiagonal(entry_coefficients,
-                                                         entry_prescribed);
-  } catch (const std::length_error&) {
-    return Result<Vector>::Failure(LoadFailure(
-        "load-backend-dimension-overflow", location, "LOAD_ASSEMBLER", "Kfc",
-        "Prescribed displacement products exceed the backend integer range."));
-  } catch (const std::invalid_argument&) {
-    return Result<Vector>::Failure(LoadFailure(
-        "invalid-load-product", location, "LOAD_ASSEMBLER", "Kfc",
-        "Prescribed displacement product inputs must be finite and compatible."));
-  }
-
-  // MKL computes independent entries; ordered CSR reduction below retains
-  // cancellation and the first product/row-sum overflow diagnostic.
-  Vector correction{kfc.Rows()};
-  for (std::size_t row = 0U; row < kfc.Rows(); ++row) {
-    double sum = 0.0;
-    for (std::size_t position = kfc.RowOffsets()[row];
-         position < kfc.RowOffsets()[row + 1U]; ++position) {
-      const double product = entry_products[position];
-      if (!std::isfinite(product)) {
-        return Result<Vector>::Failure(LoadFailure(
-            "nonfinite-load-accumulation", location, "LOAD_ASSEMBLER",
-            std::to_string(row),
-            "Kfc times prescribed displacement produced a nonfinite product."));
-      }
-      sum += product;
-      if (!std::isfinite(sum)) {
-        return Result<Vector>::Failure(LoadFailure(
-            "nonfinite-load-accumulation", location, "LOAD_ASSEMBLER",
-            std::to_string(row),
-            "Kfc times prescribed displacement produced a nonfinite row sum."));
-      }
-    }
-    correction[row] = sum;
-  }
-
-  Vector rhs = EssentialConstraintPolicy{}.GatherFree(full_load, dofs);
-  // The constrained vector is already in DofManager order, so this is the
-  // approved elimination equation rhs = Ff - Kfc*dc without reordering dc.
-  for (std::size_t row = 0U; row < rhs.Size(); ++row) {
-    const double value = rhs[row] - correction[row];
-    if (!std::isfinite(value)) {
-      return Result<Vector>::Failure(
-          LoadFailure("nonfinite-load-accumulation", location, "LOAD_ASSEMBLER",
-                      std::to_string(row),
-                      "Effective RHS subtraction produced a nonfinite value."));
-    }
-    rhs[row] = value;
-  }
-  return Result<Vector>::Success(std::move(rhs));
+  return EssentialConstraintPolicy{}.EffectiveFreeRhs(
+      full_load, kfc, prescribed_values, dofs);
 }
 
 }  // namespace fesa

src/fesa/assembly/ordered_contribution_internal.h

@@ -0,0 +1,58 @@
+#ifndef FESA_ASSEMBLY_ORDERED_CONTRIBUTION_INTERNAL_H_
+#define FESA_ASSEMBLY_ORDERED_CONTRIBUTION_INTERNAL_H_
+
+#include <cmath>
+#include <cstddef>
+#include <vector>
+
+#include "fesa/math/matrix.h"
+#include "fesa/math/sparse_matrix.h"
+#include "fesa/math/vector.h"
+
+namespace fesa::assembly_internal {
+
+/// @brief Appends one validated local entry without changing its stable order.
+/// @note Caller owns shape/scatter validation and diagnostic selection. Retains
+/// every structural zero; never writes shared global storage from a worker.
+template <class Scatter>
+void AppendLocalMatrixEntry(const Scatter& scatter, std::size_t row,
+                            std::size_t column, double value,
+                            std::size_t source_order,
+                            std::vector<CooContribution>& contributions) {
+  contributions.push_back({scatter[row], scatter[column], value, source_order,
+                           row * scatter.size() + column});
+}
+
+/// @brief Appends a validated matrix row in the original local-column order.
+template <class Scatter>
+void AppendLocalMatrixRow(const Matrix& values, const Scatter& scatter,
+                          std::size_t row, std::size_t source_order,
+                          std::vector<CooContribution>& contributions) {
+  for (std::size_t column = 0U; column < scatter.size(); ++column) {
+    AppendLocalMatrixEntry(scatter, row, column, values(row, column),
+                            source_order, contributions);
+  }
+}
+
+/// @brief Appends a validated matrix in fixed local row/column order.
+template <class Scatter>
+void AppendLocalMatrix(const Matrix& values, const Scatter& scatter,
+                       std::size_t source_order,
+                       std::vector<CooContribution>& contributions) {
+  for (std::size_t row = 0U; row < scatter.size(); ++row) {
+    AppendLocalMatrixRow(values, scatter, row, source_order, contributions);
+  }
+}
+
+/// @brief Adds one full-space load entry, committing only a finite candidate.
+/// @note Caller validates the index and keeps source-order error provenance.
+inline bool AccumulateFiniteLoad(Vector& full, std::size_t index, double value) {
+  const double accumulated = full[index] + value;
+  if (!std::isfinite(value) || !std::isfinite(accumulated)) return false;
+  full[index] = accumulated;
+  return true;
+}
+
+}  // namespace fesa::assembly_internal
+
+#endif  // FESA_ASSEMBLY_ORDERED_CONTRIBUTION_INTERNAL_H_