MemMAPR-MKE/Solver.cpp

#include "Header.h"
#include <Eigen/Dense>
using namespace Eigen;

Solver::Solver(double _A, double _B, double _C, int _N, int _l, int _u) {
    A = _A, B = _B, C = _C, N = _N;
    upper = _u, lower = _l;
	L = upper - lower;
	dx = L / N;
}

void Solver::Execute_Linear() {
    MatrixXd local = MatrixXd::Zero(2, 2);
    local(0, 0) = A / dx - B / 2;
    local(0, 1) = -A / dx + B / 2;
    local(1, 0) = -A / dx - B / 2;
    local(1, 1) = A / dx + B / 2;
    std::cout << "Local matrix:\n" << local << std::endl;

    VectorXd local_load(2);
    local_load(0) = C * dx / 2;
    local_load(1) = C * dx / 2;

    // Àíñàáëèðîâàííûå ìàòðèöû è âåêòîð
    MatrixXd ansamb = MatrixXd::Zero(N + 1, N + 1);
    VectorXd global_load = VectorXd::Zero(N + 1);

    // Àíñàìáëèðîâàíèå äëÿ êàæäîãî êîíå÷íîãî ýëåìåíòà
    for (int elem = 0; elem < N; ++elem) {
        int node_i = elem;
        int node_j = elem + 1;

        // Ìàòðèöà æåñòêîñòè
        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);

        // Âåêòîð íàãðóçêè
        global_load(node_i) += local_load(0);
        global_load(node_j) += local_load(1);
    }

    std::cout << "Before:" << std::endl;
    std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
    std::cout << "Ansamb load vector:\n" << global_load << std::endl;

    // ÃÓ 1-ãî ðîäà
    double u_left = 5.0;   // u(1) = 5
    double u_right = 15.0; // u(6) = 15

    // 1. Ó÷¸ò óñëîâèÿ u(1)=5
    for (int i = 1; i < N + 1; ++i) {
        global_load(i) -= ansamb(i, 0) * u_left;
    }
    // Îáíóëÿåì ïåðâóþ ñòðîêó è ñòîëáåö ìàòðèöû, óñòàíàâëèâàåì äèàãîíàëü = 1
    ansamb.row(0).setZero();
    ansamb.col(0).setZero();
    ansamb(0, 0) = 1.0;
    global_load(0) = u_left;

    // 2. Ó÷¸ò óñëîâèÿ u(6)=15
    for (int i = 0; i < N; ++i) {
        global_load(i) -= ansamb(i, N) * u_right;
    }
    // Îáíóëÿåì ïîñëåäíþþ ñòðîêó è ñòîëáåö ìàòðèöû, óñòàíàâëèâàåì äèàãîíàëü = 1
    ansamb.row(N).setZero();
    ansamb.col(N).setZero();
    ansamb(N, N) = 1.0;
    global_load(N) = u_right;

    std::cout << "\nAfter:" << std::endl;
    std::cout << "Modified matrix:\n" << ansamb << std::endl;
    std::cout << "Modified load vector:\n" << global_load << std::endl;

    VectorXd solution = ansamb.fullPivLu().solve(global_load);
    std::cout << "\nSolution:" << std::endl;
    std::cout << solution << std::endl;

    std::ofstream file("matrix_2.txt");
    for (int i = 0; i < N + 1; i++) {
        file << solution(i) << ' ';
    }
    file << std::endl;
}

void Solver::Execute_Cubic() {
    MatrixXd local = MatrixXd::Zero(4, 4);
    local(0, 0) = -37*A/(10*dx) - B/2;
    local(0, 1) = 189*A/(40*dx) + 57*B/80;
    local(0, 2) = -27*A/(20*dx) - 3*B/10;
    local(0, 3) = 13*A/(40*dx) + 7*B/80;

    local(1, 0) = 189/(40*dx) - 57*B/80;
    local(1, 1) = -54*A/(5*dx);
    local(1, 2) = 297*A/(40*dx) + 81*B/80;
    local(1, 3) = -20*A/(20*dx) - 3*B/10;

    local(2, 0) = -27*A / (20 * dx) + 3 * B / 10;
    local(2, 1) = 297 * A / (40 * dx) - 81*B/80;
    local(2, 2) = -54 * A / (5 * dx);
    local(2, 3) = 189*A / (40 * dx) + 57 * B / 80;

    local(3, 0) = 13*A/(40 * dx);
    local(3, 1) = -27 * A / (20 * dx) + 3 * B / 10;
    local(3, 2) = 189*A / (40 * dx) - 57 * B / 80;
    local(3, 3) = -37 * A/(10 * dx) + B/2;


    VectorXd local_load(4);
    local_load(0) = local_load(3) = -C * dx / 8;
    local_load(1) = local_load(2) = -3 * C * dx / 8;

    std::cout << "Local matrix:\n" << local << std::endl;

    // Àíñàìáëèðîâàííûå ìàòðèöà è âåêòîð
    MatrixXd ansamb = MatrixXd::Zero(N + 1, N + 1);
    VectorXd global_load = VectorXd::Zero(N + 1);

    // Àíñàìáëèðîâàíèå äëÿ êàæäîãî êîíå÷íîãî ýëåìåíòà
    //for (int elem = 0; elem < N; ++elem) {
    //    int node_i = elem;
    //    int node_j = elem + 1;

    //    // Ìàòðèöà æåñòêîñòè
    //    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);

    //    // Âåêòîð íàãðóçêè
    //    global_load(node_i) += local_load(0);
    //    global_load(node_j) += local_load(1);
    //}

    //std::cout << "Before:" << std::endl;
    //std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
    //std::cout << "Ansamb load vector:\n" << global_load << std::endl;

}