feat(equation-and-linear-solve): step 1 — essential-bc-elimination

include/fesa/constraints/essential_bc.hpp

@@ -0,0 +1,36 @@
+#pragma once
+
+#include <cstddef>
+#include <optional>
+#include <span>
+#include <vector>
+
+#include <fesa/assembly/equation_system.hpp>
+#include <fesa/core/diagnostic.hpp>
+#include <fesa/fem/dof_manager.hpp>
+#include <fesa/model/step_definition.hpp>
+
+namespace fesa {
+
+struct ReducedSystem final {
+    SymmetricCsr stiffness;
+    std::vector<double> force;
+    std::vector<std::size_t> free_to_full;
+    std::vector<double> prescribed_full;
+};
+
+struct ConstraintResult final {
+    std::optional<ReducedSystem> reduced_system;
+    std::vector<Diagnostic> diagnostics;
+};
+
+[[nodiscard]] ConstraintResult eliminate_essential_bcs(
+    const EquationSystem& original,
+    const DofManager& dofs,
+    std::span<const PrescribedDof> prescribed);
+
+[[nodiscard]] std::vector<double> recover_reaction(
+    const EquationSystem& original,
+    std::span<const double> full_displacement);
+
+}  // namespace fesa

include/fesa/fem/dof_manager.hpp

@@ -34,6 +34,8 @@ public:
     [[nodiscard]] std::size_t free_equation_count() const noexcept;
     [[nodiscard]] std::optional<std::size_t> equation(
         DofAddress address) const;
+    [[nodiscard]] std::optional<double> prescribed_value(
+        DofAddress address) const;
     [[nodiscard]] std::size_t full_dof(DofAddress address) const;
     [[nodiscard]] std::array<std::size_t, 12> element_full_dofs(
         const BeamElement& element) const;