feat(cpp-object-oriented-modular-refactoring): step 3 - foundation-google-style

include/fesa/solvers/linear/linear_solver.h

@@ -0,0 +1,30 @@
+#ifndef FESA_SOLVERS_LINEAR_LINEAR_SOLVER_H_
+#define FESA_SOLVERS_LINEAR_LINEAR_SOLVER_H_
+
+#include "fesa/core/status.h"
+
+namespace fesa {
+
+class SparseMatrix;
+class Vector;
+
+/// @brief Separates reusable factorization from RHS substitution.
+class LinearSolver {
+ public:
+  /// @brief Destroys a backend-neutral linear solver.
+  virtual ~LinearSolver() = default;
+
+  /// @brief Factorizes a validated free-equation matrix for reuse.
+  /// @return Success or a structured solver failure.
+  virtual Status Factorize(const SparseMatrix& matrix) = 0;
+
+  /// @brief Substitutes one right-hand side using retained factorization.
+  /// @param rhs Immutable right-hand side in free-equation order.
+  /// @param solution Updated only after successful finite substitution.
+  /// @return Success or a structured solver failure.
+  virtual Status Solve(const Vector& rhs, Vector& solution) const = 0;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_SOLVERS_LINEAR_LINEAR_SOLVER_H_