Решатель выделен в отдельный класс

TODO: сделать всё-таки универсальный класс
This commit is contained in:
2025-09-08 22:45:20 +03:00
parent c7ff86c752
commit 4c8880f646
6 changed files with 103 additions and 75 deletions

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@@ -1,3 +1,3 @@
#include <iostream> #include <iostream>
#include <fstream> #include <fstream>
#include <Eigen/Dense> #include "Solver.h"

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@@ -1,81 +1,10 @@
#include "Header.h" #include "Header.h"
#include "Solver.h"
using namespace Eigen;
int main() { int main() {
std::ifstream file("matrix.txt"); std::ifstream file("matrix.txt");
int N = 3; Solver slv(1., 0., 1., 3, 0, 1);
int upper = 1, lower = 0; slv.Execute();
double A = 1, B = 0, C = 1, L = upper - lower;
double dx = L / N;
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;
// Ансамблированные матрица и вектор
MatrixXd ansamb = MatrixXd::Zero(N + 1, N + 1);
VectorXd global_load = VectorXd::Zero(N + 1);
// Ансамблирование для каждого конечного элемента
for (int elem = 0; elem < N; ++elem) {
int node_i = elem;
int node_j = elem + 1;
// Матрица жесткости
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);
// Вектор нагрузки
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;
// ГУ 1-го рода
double u_left = 5.0; // u(1) = 5
double u_right = 15.0; // u(6) = 15
// 1. Учёт условия u(1)=5
for (int i = 1; i < N + 1; ++i) {
global_load(i) -= ansamb(i, 0) * u_left;
}
// Обнуляем первую строку и столбец матрицы, устанавливаем диагональ = 1
ansamb.row(0).setZero();
ansamb.col(0).setZero();
ansamb(0, 0) = 1.0;
global_load(0) = u_left;
// 2. Учёт условия u(6)=15
for (int i = 0; i < N; ++i) {
global_load(i) -= ansamb(i, N) * u_right;
}
// Обнуляем последнюю строку и столбец матрицы, устанавливаем диагональ = 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;
return 0; return 0;
} }

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@@ -124,12 +124,14 @@
</ItemDefinitionGroup> </ItemDefinitionGroup>
<ItemGroup> <ItemGroup>
<ClCompile Include="MemMAPR-MKE.cpp" /> <ClCompile Include="MemMAPR-MKE.cpp" />
<ClCompile Include="Solver.cpp" />
</ItemGroup> </ItemGroup>
<ItemGroup> <ItemGroup>
<None Include="packages.config" /> <None Include="packages.config" />
</ItemGroup> </ItemGroup>
<ItemGroup> <ItemGroup>
<ClInclude Include="Header.h" /> <ClInclude Include="Header.h" />
<ClInclude Include="Solver.h" />
</ItemGroup> </ItemGroup>
<Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" /> <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
<ImportGroup Label="ExtensionTargets"> <ImportGroup Label="ExtensionTargets">

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@@ -13,11 +13,17 @@
<UniqueIdentifier>{67DA6AB6-F800-4c08-8B7A-83BB121AAD01}</UniqueIdentifier> <UniqueIdentifier>{67DA6AB6-F800-4c08-8B7A-83BB121AAD01}</UniqueIdentifier>
<Extensions>rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms</Extensions> <Extensions>rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms</Extensions>
</Filter> </Filter>
<Filter Include="Solver">
<UniqueIdentifier>{3be6c970-16cc-463a-a3d5-22a26a8bff54}</UniqueIdentifier>
</Filter>
</ItemGroup> </ItemGroup>
<ItemGroup> <ItemGroup>
<ClCompile Include="MemMAPR-MKE.cpp"> <ClCompile Include="MemMAPR-MKE.cpp">
<Filter>Исходные файлы</Filter> <Filter>Исходные файлы</Filter>
</ClCompile> </ClCompile>
<ClCompile Include="Solver.cpp">
<Filter>Solver</Filter>
</ClCompile>
</ItemGroup> </ItemGroup>
<ItemGroup> <ItemGroup>
<None Include="packages.config" /> <None Include="packages.config" />
@@ -26,5 +32,8 @@
<ClInclude Include="Header.h"> <ClInclude Include="Header.h">
<Filter>Исходные файлы</Filter> <Filter>Исходные файлы</Filter>
</ClInclude> </ClInclude>
<ClInclude Include="Solver.h">
<Filter>Solver</Filter>
</ClInclude>
</ItemGroup> </ItemGroup>
</Project> </Project>

79
Solver.cpp Normal file
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@@ -0,0 +1,79 @@
#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() {
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;
// <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> <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><> 1-<2D><> <20><><EFBFBD><EFBFBD>
double u_left = 5.0; // u(1) = 5
double u_right = 15.0; // u(6) = 15
// 1. <20><><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> u(1)=5
for (int i = 1; i < N + 1; ++i) {
global_load(i) -= ansamb(i, 0) * u_left;
}
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> = 1
ansamb.row(0).setZero();
ansamb.col(0).setZero();
ansamb(0, 0) = 1.0;
global_load(0) = u_left;
// 2. <20><><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> u(6)=15
for (int i = 0; i < N; ++i) {
global_load(i) -= ansamb(i, N) * u_right;
}
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> = 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;
}

9
Solver.h Normal file
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@@ -0,0 +1,9 @@
#pragma once
class Solver {
private:
double A, B, C, L, dx;
int N, upper, lower;
public:
Solver(double _A, double _B, double _C, int _N, int _l, int _u);
void Execute();
};