feat(equation-and-linear-solve): step 0 — symmetric-csr-assembly

include/fesa/assembly/equation_system.hpp

@@ -0,0 +1,14 @@
+#pragma once
+
+#include <vector>
+
+#include <fesa/assembly/symmetric_csr.hpp>
+
+namespace fesa {
+
+struct EquationSystem final {
+    SymmetricCsr stiffness;
+    std::vector<double> force;
+};
+
+}  // namespace fesa

include/fesa/assembly/serial_assembler.hpp

@@ -0,0 +1,13 @@
+#pragma once
+
+#include <fesa/assembly/equation_system.hpp>
+#include <fesa/fem/dof_manager.hpp>
+#include <fesa/model/domain.hpp>
+
+namespace fesa {
+
+[[nodiscard]] EquationSystem assemble_serial(
+    const Domain& domain,
+    const DofManager& dofs);
+
+}  // namespace fesa

include/fesa/assembly/symmetric_csr.hpp

@@ -0,0 +1,18 @@
+#pragma once
+
+#include <cstddef>
+#include <cstdint>
+#include <vector>
+
+namespace fesa {
+
+// Zero-based CSR containing only the upper triangle. Column indices are
+// strictly increasing within each row.
+struct SymmetricCsr final {
+    std::size_t order;
+    std::vector<std::int32_t> row_offsets;
+    std::vector<std::int32_t> column_indices;
+    std::vector<double> values;
+};
+
+}  // namespace fesa