forked from ParkSuMin/MemMAPR-MKE
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18
src/MemMAPR-MKE.cpp
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18
src/MemMAPR-MKE.cpp
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#include "Solver.h"
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#include "Header.h"
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#include <Eigen/Dense>
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#define A 5.
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#define B 4.
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#define C 0.
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#define D 1.
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using namespace Eigen;
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int main() {
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std::cout << A << "u''" << " + " << B << "u'" << "+ " << C << "u + " << D << " = 0" << std::endl;
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Solver slv(A, B, C, D, 2, 0, 10);
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std::cout << "Linear element:";
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slv.Execute_Linear(0, 5);
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std::cout << "\nCubic element:";
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slv.Execute_Cubic(0, 5);
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return 0;
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}
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171
src/Solver.cpp
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171
src/Solver.cpp
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#include "Header.h"
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#include <Eigen/Dense>
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using namespace Eigen;
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Solver::Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u) {
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A = _A, B = _B, C = _C, D = _D, N = _N;
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upper = _u, lower = _l;
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L = (double)(upper - lower) / N;
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}
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void Solver::Execute_Linear(double val1, double val2) {
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// Локальная матрица жёсткости
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MatrixXd local = MatrixXd::Zero(2, 2);
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// Локальный вектор нагрузки
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VectorXd local_load(2);
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local(0, 0) = -A / L - B / 2. + C * L / 2.;
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local(0, 1) = A / L + B / 2. + C * L / 2.;
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local(1, 0) = A / L - B / 2. + C * L / 2.;
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local(1, 1) = -A / L + B / 2. + C * L / 2.;
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local_load(0) = -D * L / 2.;
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local_load(1) = -D * L / 2.;
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// Глобальная матрица жёсткости
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MatrixXd ansamb = MatrixXd::Zero(N + 2, N + 2);
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// Глобальный вектор нагрузок
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VectorXd global_load = VectorXd::Zero(N + 2);
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// Ансамблирование (с учётом смещения на 1)
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for (int elem = 0; elem < N; ++elem) {
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int node_i = elem + 1;
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int node_j = elem + 2;
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ansamb(node_i, node_i) += local(0, 0);
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ansamb(node_i, node_j) += local(0, 1);
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ansamb(node_j, node_i) += local(1, 0);
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ansamb(node_j, node_j) += local(1, 1);
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global_load(node_i) += local_load(0);
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global_load(node_j) += local_load(1);
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}
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#if DEBUG
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std::cout << std::endl << "Before:" << std::endl;
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std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
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std::cout << "Ansamb load vector:\n" << global_load << std::endl;
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#endif
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// Граничные условия
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double u_right = val2;
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ansamb.row(0).setZero();
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ansamb(0, 0) = 1;
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ansamb(0, 1) = -1;
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global_load(0) = 0;
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ansamb(1, 1) -= A;
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ansamb.row(N + 1).setZero();
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ansamb(N + 1, N + 1) = 1;
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global_load(N + 1) = u_right;
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#if DEBUG
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std::cout << "\nAfter:" << std::endl;
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std::cout << "Modified matrix:\n" << ansamb << std::endl;
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std::cout << "Modified load vector:\n" << global_load << std::endl;
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#endif
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// Решение системы
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VectorXd solution = ansamb.fullPivLu().solve(global_load);
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std::cout << "\nSolution:" << std::endl;
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std::cout << solution << std::endl;
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std::ofstream file("matrix_linear_" + std::to_string(N) + ".txt");
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for (int i = 1; i < solution.size(); i++) {
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file << solution(i) << ' ';
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}
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file << std::endl;
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}
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void Solver::Execute_Cubic(double val1, double val2) {
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int mat_dim = N * 3 + 2; // +2 для граничных узлов, как в линейном случае
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// Локальная матрица жёсткости
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MatrixXd local = MatrixXd::Zero(4, 4);
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// Локальный вектор нагрузки
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VectorXd local_load(4);
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// Формирование локальной матрицы жёсткости
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local(0, 0) = -A * 37.0 / 10.0 / L + B * (-1.0) / 2.0 + C * 8. * L / 105.;
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local(0, 1) = -A * (-189.0) / 40.0 / L + B * 57.0 / 80.0 + C * 33. * L / 560.;
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local(0, 2) = -A * 27.0 / 20.0 / L + B * (-3.0) / 10.0 - C * 3. * L / 140.;
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local(0, 3) = -A * (-13.0) / 40.0 / L + B * 7.0 / 80.0 + C * 19. * L / 1680.;
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local(1, 0) = -A * (-189.0) / 40.0 / L + B * (-57.0) / 80.0 + C * 33. * L / 560.;
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local(1, 1) = -A * 54.0 / 5.0 / L + C * 27. * L / 70.;
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local(1, 2) = -A * (-297.0) / 40.0 / L + B * 81.0 / 80.0 - C * 27. * L / 560.;
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local(1, 3) = -A * 27.0 / 20.0 / L + B * (-3.0) / 10.0 - C * 3. * L / 140.;
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local(2, 0) = -A * 27.0 / 20.0 / L + B * 3.0 / 10.0 - C * 3. * L / 140.;
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local(2, 1) = -A * (-297.0) / 40.0 / L + B * (-81.0) / 80.0 - C * 27. * L / 560.;
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local(2, 2) = -A * 54.0 / 5.0 / L + C * 27. * L / 70.;
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local(2, 3) = -A * (-189.0) / 40.0 / L + B * 57.0 / 80.0 + C * 33. * L / 560.;
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local(3, 0) = -A * (-13.0) / 40.0 / L + B * (-7.0) / 80.0 + C * 19. * L / 1680.;
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local(3, 1) = -A * 27.0 / 20.0 / L + B * 3.0 / 10.0 - C * 3. * L / 140.;
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local(3, 2) = -A * (-189.0) / 40.0 / L + B * (-57.0) / 80.0 + C * 33. * L / 560.;
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local(3, 3) = -A * 37.0 / 10.0 / L + B * 1.0 / 2.0 + C * 8. * L / 105.;
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// Локальный вектор нагрузки
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local_load(0) = -D * L / 8.0;
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local_load(1) = -D * 3.0 * L / 8.0;
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local_load(2) = -D * 3.0 * L / 8.0;
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local_load(3) = -D * L / 8.0;
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// Глобальные матрицы
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MatrixXd ansamb = MatrixXd::Zero(mat_dim, mat_dim);
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VectorXd global_load = VectorXd::Zero(mat_dim);
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// Ансамблирование (со смещением на 1, как в линейной версии)
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for (int elem = 0; elem < N; ++elem) {
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int node_i = 1 + elem * 3; // смещение на 1
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for (int i = 0; i < 4; ++i) {
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for (int j = 0; j < 4; ++j) {
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ansamb(node_i + i, node_i + j) += local(i, j);
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}
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global_load(node_i + i) += local_load(i);
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}
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}
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#if DEBUG
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std::cout << std::endl << "Before:" << std::endl;
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std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
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std::cout << "Ansamb load vector:\n" << global_load << std::endl;
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#endif
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// Граничные условия
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double u_right = val2;
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ansamb.row(0).setZero();
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ansamb(0, 0) = 1;
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ansamb(0, 1) = -1;
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global_load(0) = 0;
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ansamb(1, 1) -= A;
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ansamb.row(mat_dim - 1).setZero();
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ansamb(mat_dim - 1, mat_dim - 1) = 1;
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global_load(mat_dim - 1) = u_right;
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#if DEBUG
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std::cout << "\nAfter:" << std::endl;
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std::cout << "Modified matrix:\n" << ansamb << std::endl;
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std::cout << "Modified load vector:\n" << global_load << std::endl;
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#endif
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// Решение системы
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VectorXd solution = ansamb.fullPivLu().solve(global_load);
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std::cout << "\nSolution:" << std::endl;
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std::cout << solution << std::endl;
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std::ofstream file("matrix_cubic_" + std::to_string(N) + ".txt");
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for (int i = 1; i < solution.size(); i++) {
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file << solution(i) << ' ';
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}
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file << std::endl;
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}
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