refactor: extract math solver boundary

include/fesa/Math/DenseMatrix.hpp

@@ -0,0 +1,53 @@
+#pragma once
+
+#include "fesa/Core/Types.hpp"
+
+#include <cstddef>
+#include <vector>
+
+namespace fesa {
+
+class DenseMatrix {
+ public:
+  DenseMatrix() = default;
+  DenseMatrix(LocalIndex rows, LocalIndex cols) : rows_(rows), cols_(cols), values_(static_cast<std::size_t>(rows * cols), 0.0) {}
+
+  LocalIndex rows() const {
+    return rows_;
+  }
+
+  LocalIndex cols() const {
+    return cols_;
+  }
+
+  Real& operator()(LocalIndex row, LocalIndex col) {
+    return values_[static_cast<std::size_t>(row * cols_ + col)];
+  }
+
+  Real operator()(LocalIndex row, LocalIndex col) const {
+    return values_[static_cast<std::size_t>(row * cols_ + col)];
+  }
+
+  void add(LocalIndex row, LocalIndex col, Real value) {
+    (*this)(row, col) += value;
+  }
+
+  std::vector<Real> multiply(const std::vector<Real>& x) const {
+    std::vector<Real> y(static_cast<std::size_t>(rows_), 0.0);
+    for (LocalIndex i = 0; i < rows_; ++i) {
+      Real sum = 0.0;
+      for (LocalIndex j = 0; j < cols_; ++j) {
+        sum += (*this)(i, j) * x[static_cast<std::size_t>(j)];
+      }
+      y[static_cast<std::size_t>(i)] = sum;
+    }
+    return y;
+  }
+
+ private:
+  LocalIndex rows_ = 0;
+  LocalIndex cols_ = 0;
+  std::vector<Real> values_;
+};
+
+}  // namespace fesa