153 lines
4.6 KiB
C++
153 lines
4.6 KiB
C++
#include "Header.h"
|
|
#include <Eigen/Dense>
|
|
using namespace Eigen;
|
|
|
|
Solver::Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u) {
|
|
A = _A, B = _B, C = _C, D = _D, N = _N;
|
|
upper = _u, lower = _l;
|
|
L = upper - lower;
|
|
dx = L / N;
|
|
}
|
|
|
|
void Solver::Execute_Linear(double val1, double val2) {
|
|
|
|
MatrixXd local = MatrixXd::Zero(2, 2);
|
|
VectorXd local_load(2);
|
|
|
|
local(0, 0) = -A / dx - B / 2. + C * dx / 3.;
|
|
local(0, 1) = A / dx + B / 2. + C * dx / 6.;
|
|
local(1, 0) = A / dx - B / 2. + C * dx / 6.;
|
|
local(1, 1) = -A / dx + B / 2. + C * dx / 3.;
|
|
|
|
local_load(0) = -D * dx / 2.;
|
|
local_load(1) = -D * dx / 2.;
|
|
|
|
MatrixXd ansamb = MatrixXd::Zero(N + 1, N + 1);
|
|
VectorXd global_load = VectorXd::Zero(N + 1);
|
|
|
|
// Ансамблирование
|
|
for (int elem = 0; elem < N; ++elem) {
|
|
int node_i = elem;
|
|
int node_j = elem + 1;
|
|
|
|
ansamb(node_i, node_i) += local(0, 0);
|
|
ansamb(node_i, node_j) += local(0, 1);
|
|
ansamb(node_j, node_i) += local(1, 0);
|
|
ansamb(node_j, node_j) += local(1, 1);
|
|
|
|
global_load(node_i) += local_load(0);
|
|
global_load(node_j) += local_load(1);
|
|
}
|
|
|
|
#if DEBUG
|
|
std::cout << std::endl << "Before:" << std::endl;
|
|
std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
|
|
std::cout << "Ansamb load vector:\n" << global_load << std::endl;
|
|
#endif
|
|
|
|
double u_right = val2;
|
|
|
|
// Clear first and last rows
|
|
ansamb.row(0).setZero();
|
|
ansamb.row(N).setZero();
|
|
|
|
// u'(0) = u(0)
|
|
ansamb(0, 0) = dx + 1;
|
|
ansamb(0, 1) = -1;
|
|
global_load(0) = 0;
|
|
|
|
// u(10) = u_right = 5
|
|
ansamb(N, N) = 1;
|
|
global_load(N) = u_right;
|
|
|
|
#if DEBUG
|
|
std::cout << "\nAfter:" << std::endl;
|
|
std::cout << "Modified matrix:\n" << ansamb << std::endl;
|
|
std::cout << "Modified load vector:\n" << global_load << std::endl;
|
|
#endif
|
|
|
|
VectorXd solution = ansamb.fullPivLu().solve(global_load);
|
|
std::cout << "\nSolution:" << std::endl;
|
|
std::cout << solution << std::endl;
|
|
|
|
std::ofstream file("matrix_linear.txt");
|
|
for (int i = 0; i < N; i++) {
|
|
file << solution(i) << ' ';
|
|
}
|
|
file << std::endl;
|
|
}
|
|
|
|
void Solver::Execute_Cubic(double val1, double val2) {
|
|
|
|
int mat_dim = 1 + N * 3;
|
|
Eigen::MatrixXd Amat(mat_dim, mat_dim);
|
|
Eigen::VectorXd b(mat_dim);
|
|
Amat.setZero();
|
|
b.setZero();
|
|
|
|
// Assemble matrix
|
|
for (int i = 0; i < mat_dim - 3; i += 3) {
|
|
Amat(i, i + 0) -= A * 37.0 / 10.0 / dx;
|
|
Amat(i, i + 1) -= A * (-189.0) / 40.0 / dx;
|
|
Amat(i, i + 2) -= A * 27.0 / 20.0 / dx;
|
|
Amat(i, i + 3) -= A * (-13.0) / 40.0 / dx;
|
|
Amat(i + 1, i + 0) -= A * (-189.0) / 40.0 / dx;
|
|
Amat(i + 1, i + 1) -= A * 54.0 / 5.0 / dx;
|
|
Amat(i + 1, i + 2) -= A * (-297.0) / 40.0 / dx;
|
|
Amat(i + 1, i + 3) -= A * 27.0 / 20.0 / dx;
|
|
Amat(i + 2, i + 0) -= A * 27.0 / 20.0 / dx;
|
|
Amat(i + 2, i + 1) -= A * (-297.0) / 40.0 / dx;
|
|
Amat(i + 2, i + 2) -= A * 54.0 / 5.0 / dx;
|
|
Amat(i + 2, i + 3) -= A * (-189.0) / 40.0 / dx;
|
|
Amat(i + 3, i + 0) -= A * (-13.0) / 40.0 / dx;
|
|
Amat(i + 3, i + 1) -= A * 27.0 / 20.0 / dx;
|
|
Amat(i + 3, i + 2) -= A * (-189.0) / 40.0 / dx;
|
|
Amat(i + 3, i + 3) -= A * 37.0 / 10.0 / dx;
|
|
|
|
Amat(i + 0, i + 0) += B * (-1.0) / 2.0;
|
|
Amat(i + 0, i + 1) += B * 57.0 / 80.0;
|
|
Amat(i + 0, i + 2) += B * (-3.0) / 10.0;
|
|
Amat(i + 0, i + 3) += B * 7.0 / 80.0;
|
|
Amat(i + 1, i + 0) += B * (-57.0) / 80.0;
|
|
|
|
Amat(i + 1, i + 2) += B * 81.0 / 80.0;
|
|
Amat(i + 1, i + 3) += B * (-3.0) / 10;
|
|
Amat(i + 2, i + 0) += B * 3.0 / 10.0;
|
|
Amat(i + 2, i + 1) += B * (-81.0) / 80.0;
|
|
|
|
Amat(i + 2, i + 3) += B * 57.0 / 80.0;
|
|
Amat(i + 3, i + 0) += B * (-7.0) / 80.0;
|
|
Amat(i + 3, i + 1) += B * 3.0 / 10.0;
|
|
Amat(i + 3, i + 2) += B * (-57.0) / 80.0;
|
|
Amat(i + 3, i + 3) += B * 1.0 / 2.0;
|
|
}
|
|
|
|
// Assembdxe vector
|
|
for (int i = 0; i < mat_dim - 3; i += 3) {
|
|
b(i) -= D * dx / 8.0;
|
|
b(i + 1) -= D * 3.0 * dx / 8.0;
|
|
b(i + 2) -= D * 3.0 * dx / 8.0;
|
|
b(i + 3) -= D * dx / 8.0;
|
|
}
|
|
|
|
|
|
Amat.row(0).setZero();
|
|
Amat(0, 0) = dx / 3.0 + 1;
|
|
Amat(0, 1) = -1;
|
|
b(0) = 0;
|
|
|
|
Amat.row(mat_dim - 1).setZero();
|
|
Amat(mat_dim - 1, mat_dim - 1) = 1;
|
|
b(mat_dim - 1) = val2;
|
|
|
|
// Решение системы
|
|
VectorXd solution = Amat.colPivHouseholderQr().solve(b);
|
|
std::cout << "\nSolution:" << std::endl;
|
|
std::cout << solution << std::endl;
|
|
|
|
std::ofstream file("matrix_cubic.txt");
|
|
for (int i = 0; i < solution.size(); i++) {
|
|
file << solution(i) << ' ';
|
|
}
|
|
file << std::endl;
|
|
} |