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Возможно корректное решение при помощи кубического КЭ

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ParkSuMin
2025-09-10 21:02:45 +03:00
parent 85cd9c0dd0
commit 274d59e659
1 changed files with 81 additions and 38 deletions
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99
Solver.cpp
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@@ -46,8 +46,8 @@ void Solver::Execute_Linear() {
std::cout << "Ansamb load vector:\n" << global_load << std::endl;
// <20><> 1-<2D><> <20><><EFBFBD><EFBFBD>
double u_left = 5.0; // u(1) = 5
double u_right = 15.0; // u(6) = 15
double u_left = -5.0; // u(1) = 5
double u_right = -10.0; // u(6) = 15
// 1. <20><><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> u(1)=5
for (int i = 1; i < N + 1; ++i) {
@@ -85,13 +85,14 @@ void Solver::Execute_Linear() {
}
void Solver::Execute_Cubic() {
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> (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/(40*dx) - 57*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;
@@ -106,35 +107,77 @@ void Solver::Execute_Cubic() {
local(3, 2) = 189 * A / (40 * dx) - 57 * B / 80;
local(3, 3) = -37 * A / (10 * dx) + B / 2;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> (4x1)
VectorXd local_load(4);
local_load(0) = local_load(3) = -C * dx / 8;
local_load(1) = local_load(2) = -3 * C * dx / 8;
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;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
MatrixXd ansamb = MatrixXd::Zero(N + 1, N + 1);
VectorXd global_load = VectorXd::Zero(N + 1);
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>: <20><><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> (4 <20><><EFBFBD><EFBFBD> <20><> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><> 2 <20><><EFBFBD><EFBFBD>)
int ndof = 2 * N + 2;
MatrixXd ansamb = MatrixXd::Zero(ndof, ndof);
VectorXd global_load = VectorXd::Zero(ndof);
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
//for (int elem = 0; elem < N; ++elem) {
// int node_i = elem;
// int node_j = elem + 1;
// // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// 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);
// // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// 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;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
for (int elem = 0; elem < N; ++elem) {
int node_start = 2 * elem; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
ansamb(node_start + i, node_start + j) += local(i, j);
}
}
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
double u_left = -5.0; // u(1) = 5
double u_right = -10.0; // u(6) = 15
// <20><><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
VectorXd solution = ansamb.fullPivLu().solve(global_load);
std::cout << "\nSolution:" << std::endl;
std::cout << solution << std::endl;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> (<28><><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20> <20><><EFBFBD><EFBFBD><EFBFBD>, <20><><EFBFBD> 2)
std::ofstream file("matrix_cubic.txt");
for (int i = 0; i < ndof; i += 2) {
file << solution(i) << ' ';
}
file << std::endl;
}