feat: add solver core skeleton

tests/unit/analysis_flow_template_test.cpp

@@ -0,0 +1,44 @@
+#include <fesa/analysis/analysis.hpp>
+
+#include <string>
+#include <vector>
+
+class RecordingAnalysis : public fesa::analysis::Analysis {
+public:
+    const std::vector<std::string>& calls() const
+    {
+        return calls_;
+    }
+
+protected:
+    void initialize() override { calls_.push_back("initialize"); }
+    void build_analysis_model() override { calls_.push_back("build_analysis_model"); }
+    void build_dof_map() override { calls_.push_back("build_dof_map"); }
+    void build_sparse_pattern() override { calls_.push_back("build_sparse_pattern"); }
+    void assemble() override { calls_.push_back("assemble"); }
+    void apply_boundary_conditions() override { calls_.push_back("apply_boundary_conditions"); }
+    void solve() override { calls_.push_back("solve"); }
+    void update_state() override { calls_.push_back("update_state"); }
+    void write_results() override { calls_.push_back("write_results"); }
+
+private:
+    std::vector<std::string> calls_;
+};
+
+int main()
+{
+    RecordingAnalysis analysis;
+    analysis.run();
+    const std::vector<std::string> expected{
+        "initialize",
+        "build_analysis_model",
+        "build_dof_map",
+        "build_sparse_pattern",
+        "assemble",
+        "apply_boundary_conditions",
+        "solve",
+        "update_state",
+        "write_results"
+    };
+    return analysis.calls() == expected ? 0 : 1;
+}