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 = -10.0; // 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() {
    // Ëîêàëüíàÿ ìàòðèöà æåñòêîñòè (4x4)
    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 * A / (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;

    // Ëîêàëüíûé âåêòîð íàãðóçêè (4x1)
    VectorXd local_load(4);
    local_load(0) = -C * dx / 8;
    local_load(1) = -3 * C * dx / 8;
    local_load(2) = -3 * C * dx / 8;
    local_load(3) = -C * dx / 8;

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

    // Ðàçìåð ãëîáàëüíîé ñèñòåìû: äëÿ êóáè÷åñêèõ ýëåìåíòîâ (4 óçëà íà ýëåìåíò, ïåðåêðûòèå ïî 2 óçëà)
    int ndof = 2 * N + 2;
    MatrixXd ansamb = MatrixXd::Zero(ndof, ndof);
    VectorXd global_load = VectorXd::Zero(ndof);

    // ÀÍÑÀÌÁËÈÐÎÂÀÍÈÅ
    for (int elem = 0; elem < N; ++elem) {
        int node_start = 2 * elem; // Íà÷àëüíûé èíäåêñ äëÿ òåêóùåãî ýëåìåíòà

        // Äîáàâëÿåì ëîêàëüíóþ ìàòðèöó
        for (int i = 0; i < 4; ++i) {
            for (int j = 0; j < 4; ++j) {
                ansamb(node_start + i, node_start + j) += local(i, j);
            }
        }

        // Äîáàâëÿåì ëîêàëüíûé âåêòîð íàãðóçêè
        for (int i = 0; i < 4; ++i) {
            global_load(node_start + i) += local_load(i);
        }
    }

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

    // ÃÐÀÍÈ×ÍÛÅ ÓÑËÎÂÈß
    double u_left = -5.0;   // u(1) = 5
    double u_right = -10.0; // u(6) = 15

    // Ëåâàÿ ãðàíèöà
    for (int i = 1; i < ndof; ++i) {
        global_load(i) -= ansamb(i, 0) * u_left;
    }
    ansamb.row(0).setZero();
    ansamb.col(0).setZero();
    ansamb(0, 0) = 1.0;
    global_load(0) = u_left;

    // Ïðàâàÿ ãðàíèöà
    for (int i = 0; i < ndof - 1; ++i) {
        global_load(i) -= ansamb(i, ndof - 1) * u_right;
    }
    ansamb.row(ndof - 1).setZero();
    ansamb.col(ndof - 1).setZero();
    ansamb(ndof - 1, ndof - 1) = 1.0;
    global_load(ndof - 1) = u_right;

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

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

    // Ñîõðàíåíèå ðåçóëüòàòîâ (áåðåì òîëüêî çíà÷åíèÿ ôóíêöèè â óçëàõ, øàã 2)
    std::ofstream file("matrix_cubic.txt");
    for (int i = 0; i < ndof; i += 2) {
        file << solution(i) << ' ';
    }
    file << std::endl;
}