feat(nonlinear-static-newton-raphson): step 6 - backend-neutral-tangent-solver

include/fesa/solvers/linear/tangent_solver.h

@@ -0,0 +1,31 @@
+#ifndef FESA_SOLVERS_LINEAR_TANGENT_SOLVER_H_
+#define FESA_SOLVERS_LINEAR_TANGENT_SOLVER_H_
+
+#include "fesa/core/status.h"
+
+namespace fesa {
+
+class SparseMatrix;
+class Vector;
+
+/// @brief Factorizes one nonlinear tangent and solves its correction.
+class TangentSolver {
+ public:
+  /// @brief Destroys a backend-neutral nonlinear tangent solver.
+  virtual ~TangentSolver() = default;
+
+  /// @brief Replaces any retained state with a fresh tangent factorization.
+  /// @return Success or a structured solver failure.
+  virtual Status FactorizeFresh(const SparseMatrix& matrix) = 0;
+
+  /// @brief Solves one correction using the current tangent factorization.
+  /// @param rhs Immutable free-DOF residual right-hand side.
+  /// @param correction Updated only after successful finite substitution.
+  /// @return Success or a structured solver failure.
+  virtual Status SolveCorrection(const Vector& rhs, Vector& correction) const =
+      0;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_SOLVERS_LINEAR_TANGENT_SOLVER_H_