Compare commits
22 Commits
e53cef771a
...
fix
| Author | SHA1 | Date | |
|---|---|---|---|
| 9b80340998 | |||
| 5b2331445c | |||
| e3c7b88dfb | |||
| 64cb04388a | |||
| b07c9e6cea | |||
| 1585c76980 | |||
| 1fc2925f8f | |||
| 8957f65064 | |||
| cac280deb1 | |||
| b8bc3f705a | |||
| 4fe90394ec | |||
| abe142a1d6 | |||
| faa2802f8c | |||
| 6d5ce32ca3 | |||
| 2ac0141c60 | |||
| 5a74b84c1d | |||
| 181e0874a6 | |||
| babcf0b877 | |||
| af1950982b | |||
| 5a8c3357ca | |||
| 4ab15cb13b | |||
| dc0df855d7 |
3
.gitignore
vendored
3
.gitignore
vendored
@@ -636,4 +636,7 @@ FodyWeavers.xsd
|
||||
*.msix
|
||||
*.msm
|
||||
*.msp
|
||||
|
||||
*.txt
|
||||
!CMakeLists.txt
|
||||
*.png
|
||||
|
||||
@@ -1,11 +0,0 @@
|
||||
#include "Header.h"
|
||||
#include "Solver.h"
|
||||
|
||||
int main() {
|
||||
Solver slv(3., 2., 5., 20, 1, 6);
|
||||
std::cout << "Linear element:" << std::endl;
|
||||
slv.Execute_Linear(-5, -10);
|
||||
std::cout << "\nCubic element:" << std::endl;
|
||||
slv.Execute_Cubic(-5, -10);
|
||||
return 0;
|
||||
}
|
||||
@@ -1,18 +1,24 @@
|
||||
|
||||
Microsoft Visual Studio Solution File, Format Version 12.00
|
||||
# Visual Studio Version 17
|
||||
VisualStudioVersion = 17.14.36310.24 d17.14
|
||||
VisualStudioVersion = 17.14.36310.24
|
||||
MinimumVisualStudioVersion = 10.0.40219.1
|
||||
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "MemMAPR-MKE", "MemMAPR-MKE.vcxproj", "{5D2C9737-E669-4AF1-9B8C-4339EF6E4EB0}"
|
||||
EndProject
|
||||
Global
|
||||
GlobalSection(SolutionConfigurationPlatforms) = preSolution
|
||||
DEBUG_THIRD|x64 = DEBUG_THIRD|x64
|
||||
DEBUG_THIRD|x86 = DEBUG_THIRD|x86
|
||||
Debug|x64 = Debug|x64
|
||||
Debug|x86 = Debug|x86
|
||||
Release|x64 = Release|x64
|
||||
Release|x86 = Release|x86
|
||||
EndGlobalSection
|
||||
GlobalSection(ProjectConfigurationPlatforms) = postSolution
|
||||
{5D2C9737-E669-4AF1-9B8C-4339EF6E4EB0}.DEBUG_THIRD|x64.ActiveCfg = DEBUG_FIRST|x64
|
||||
{5D2C9737-E669-4AF1-9B8C-4339EF6E4EB0}.DEBUG_THIRD|x64.Build.0 = DEBUG_FIRST|x64
|
||||
{5D2C9737-E669-4AF1-9B8C-4339EF6E4EB0}.DEBUG_THIRD|x86.ActiveCfg = DEBUG_FIRST|Win32
|
||||
{5D2C9737-E669-4AF1-9B8C-4339EF6E4EB0}.DEBUG_THIRD|x86.Build.0 = DEBUG_FIRST|Win32
|
||||
{5D2C9737-E669-4AF1-9B8C-4339EF6E4EB0}.Debug|x64.ActiveCfg = Debug|x64
|
||||
{5D2C9737-E669-4AF1-9B8C-4339EF6E4EB0}.Debug|x64.Build.0 = Debug|x64
|
||||
{5D2C9737-E669-4AF1-9B8C-4339EF6E4EB0}.Debug|x86.ActiveCfg = Debug|Win32
|
||||
|
||||
@@ -1,6 +1,14 @@
|
||||
<?xml version="1.0" encoding="utf-8"?>
|
||||
<Project DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
|
||||
<ItemGroup Label="ProjectConfigurations">
|
||||
<ProjectConfiguration Include="DEBUG_FIRST|Win32">
|
||||
<Configuration>DEBUG_FIRST</Configuration>
|
||||
<Platform>Win32</Platform>
|
||||
</ProjectConfiguration>
|
||||
<ProjectConfiguration Include="DEBUG_FIRST|x64">
|
||||
<Configuration>DEBUG_FIRST</Configuration>
|
||||
<Platform>x64</Platform>
|
||||
</ProjectConfiguration>
|
||||
<ProjectConfiguration Include="Debug|Win32">
|
||||
<Configuration>Debug</Configuration>
|
||||
<Platform>Win32</Platform>
|
||||
@@ -32,6 +40,12 @@
|
||||
<PlatformToolset>v143</PlatformToolset>
|
||||
<CharacterSet>Unicode</CharacterSet>
|
||||
</PropertyGroup>
|
||||
<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='DEBUG_FIRST|Win32'" Label="Configuration">
|
||||
<ConfigurationType>Application</ConfigurationType>
|
||||
<UseDebugLibraries>true</UseDebugLibraries>
|
||||
<PlatformToolset>v143</PlatformToolset>
|
||||
<CharacterSet>Unicode</CharacterSet>
|
||||
</PropertyGroup>
|
||||
<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|Win32'" Label="Configuration">
|
||||
<ConfigurationType>Application</ConfigurationType>
|
||||
<UseDebugLibraries>false</UseDebugLibraries>
|
||||
@@ -45,6 +59,12 @@
|
||||
<PlatformToolset>v143</PlatformToolset>
|
||||
<CharacterSet>Unicode</CharacterSet>
|
||||
</PropertyGroup>
|
||||
<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='DEBUG_FIRST|x64'" Label="Configuration">
|
||||
<ConfigurationType>Application</ConfigurationType>
|
||||
<UseDebugLibraries>true</UseDebugLibraries>
|
||||
<PlatformToolset>v143</PlatformToolset>
|
||||
<CharacterSet>Unicode</CharacterSet>
|
||||
</PropertyGroup>
|
||||
<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|x64'" Label="Configuration">
|
||||
<ConfigurationType>Application</ConfigurationType>
|
||||
<UseDebugLibraries>false</UseDebugLibraries>
|
||||
@@ -60,12 +80,18 @@
|
||||
<ImportGroup Label="PropertySheets" Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">
|
||||
<Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
|
||||
</ImportGroup>
|
||||
<ImportGroup Condition="'$(Configuration)|$(Platform)'=='DEBUG_FIRST|Win32'" Label="PropertySheets">
|
||||
<Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
|
||||
</ImportGroup>
|
||||
<ImportGroup Label="PropertySheets" Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">
|
||||
<Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
|
||||
</ImportGroup>
|
||||
<ImportGroup Label="PropertySheets" Condition="'$(Configuration)|$(Platform)'=='Debug|x64'">
|
||||
<Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
|
||||
</ImportGroup>
|
||||
<ImportGroup Condition="'$(Configuration)|$(Platform)'=='DEBUG_FIRST|x64'" Label="PropertySheets">
|
||||
<Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
|
||||
</ImportGroup>
|
||||
<ImportGroup Label="PropertySheets" Condition="'$(Configuration)|$(Platform)'=='Release|x64'">
|
||||
<Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
|
||||
</ImportGroup>
|
||||
@@ -82,6 +108,18 @@
|
||||
<GenerateDebugInformation>true</GenerateDebugInformation>
|
||||
</Link>
|
||||
</ItemDefinitionGroup>
|
||||
<ItemDefinitionGroup Condition="'$(Configuration)|$(Platform)'=='DEBUG_FIRST|Win32'">
|
||||
<ClCompile>
|
||||
<WarningLevel>Level3</WarningLevel>
|
||||
<SDLCheck>true</SDLCheck>
|
||||
<PreprocessorDefinitions>WIN32;_DEBUG;_CONSOLE;%(PreprocessorDefinitions)</PreprocessorDefinitions>
|
||||
<ConformanceMode>true</ConformanceMode>
|
||||
</ClCompile>
|
||||
<Link>
|
||||
<SubSystem>Console</SubSystem>
|
||||
<GenerateDebugInformation>true</GenerateDebugInformation>
|
||||
</Link>
|
||||
</ItemDefinitionGroup>
|
||||
<ItemDefinitionGroup Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">
|
||||
<ClCompile>
|
||||
<WarningLevel>Level3</WarningLevel>
|
||||
@@ -100,8 +138,26 @@
|
||||
<ClCompile>
|
||||
<WarningLevel>Level3</WarningLevel>
|
||||
<SDLCheck>true</SDLCheck>
|
||||
<PreprocessorDefinitions>_DEBUG;_CONSOLE;%(PreprocessorDefinitions)</PreprocessorDefinitions>
|
||||
<PreprocessorDefinitions>DEBUG;_CONSOLE;%(PreprocessorDefinitions)</PreprocessorDefinitions>
|
||||
<ConformanceMode>true</ConformanceMode>
|
||||
<LanguageStandard>Default</LanguageStandard>
|
||||
<LanguageStandard_C>Default</LanguageStandard_C>
|
||||
<AdditionalIncludeDirectories>include/</AdditionalIncludeDirectories>
|
||||
</ClCompile>
|
||||
<Link>
|
||||
<SubSystem>Console</SubSystem>
|
||||
<GenerateDebugInformation>true</GenerateDebugInformation>
|
||||
</Link>
|
||||
</ItemDefinitionGroup>
|
||||
<ItemDefinitionGroup Condition="'$(Configuration)|$(Platform)'=='DEBUG_FIRST|x64'">
|
||||
<ClCompile>
|
||||
<WarningLevel>Level3</WarningLevel>
|
||||
<SDLCheck>true</SDLCheck>
|
||||
<PreprocessorDefinitions>DEBUG;_CONSOLE;THIRD;%(PreprocessorDefinitions)</PreprocessorDefinitions>
|
||||
<ConformanceMode>true</ConformanceMode>
|
||||
<LanguageStandard>Default</LanguageStandard>
|
||||
<LanguageStandard_C>Default</LanguageStandard_C>
|
||||
<AdditionalIncludeDirectories>include/</AdditionalIncludeDirectories>
|
||||
</ClCompile>
|
||||
<Link>
|
||||
<SubSystem>Console</SubSystem>
|
||||
@@ -116,6 +172,9 @@
|
||||
<SDLCheck>true</SDLCheck>
|
||||
<PreprocessorDefinitions>NDEBUG;_CONSOLE;%(PreprocessorDefinitions)</PreprocessorDefinitions>
|
||||
<ConformanceMode>true</ConformanceMode>
|
||||
<LanguageStandard>Default</LanguageStandard>
|
||||
<LanguageStandard_C>Default</LanguageStandard_C>
|
||||
<AdditionalIncludeDirectories>include/</AdditionalIncludeDirectories>
|
||||
</ClCompile>
|
||||
<Link>
|
||||
<SubSystem>Console</SubSystem>
|
||||
@@ -123,15 +182,15 @@
|
||||
</Link>
|
||||
</ItemDefinitionGroup>
|
||||
<ItemGroup>
|
||||
<ClCompile Include="MemMAPR-MKE.cpp" />
|
||||
<ClCompile Include="Solver.cpp" />
|
||||
<ClCompile Include="src\MemMAPR-MKE.cpp" />
|
||||
<ClCompile Include="src\Solver.cpp" />
|
||||
</ItemGroup>
|
||||
<ItemGroup>
|
||||
<None Include="packages.config" />
|
||||
</ItemGroup>
|
||||
<ItemGroup>
|
||||
<ClInclude Include="Header.h" />
|
||||
<ClInclude Include="Solver.h" />
|
||||
<ClInclude Include="include\Header.h" />
|
||||
<ClInclude Include="include\Solver.h" />
|
||||
</ItemGroup>
|
||||
<Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
|
||||
<ImportGroup Label="ExtensionTargets">
|
||||
|
||||
@@ -18,22 +18,22 @@
|
||||
</Filter>
|
||||
</ItemGroup>
|
||||
<ItemGroup>
|
||||
<ClCompile Include="MemMAPR-MKE.cpp">
|
||||
<Filter>Исходные файлы</Filter>
|
||||
</ClCompile>
|
||||
<ClCompile Include="Solver.cpp">
|
||||
<ClCompile Include="src\Solver.cpp">
|
||||
<Filter>Solver</Filter>
|
||||
</ClCompile>
|
||||
<ClCompile Include="src\MemMAPR-MKE.cpp">
|
||||
<Filter>Исходные файлы</Filter>
|
||||
</ClCompile>
|
||||
</ItemGroup>
|
||||
<ItemGroup>
|
||||
<None Include="packages.config" />
|
||||
</ItemGroup>
|
||||
<ItemGroup>
|
||||
<ClInclude Include="Header.h">
|
||||
<Filter>Исходные файлы</Filter>
|
||||
</ClInclude>
|
||||
<ClInclude Include="Solver.h">
|
||||
<ClInclude Include="include\Solver.h">
|
||||
<Filter>Solver</Filter>
|
||||
</ClInclude>
|
||||
<ClInclude Include="include\Header.h">
|
||||
<Filter>Исходные файлы</Filter>
|
||||
</ClInclude>
|
||||
</ItemGroup>
|
||||
</Project>
|
||||
167
Solver.cpp
167
Solver.cpp
@@ -1,167 +0,0 @@
|
||||
#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(double val1, double val2) {
|
||||
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;
|
||||
|
||||
// Ансаблированные матрицы 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 = val1; // u(1) = 5
|
||||
double u_right = val2; // u(6) = 15
|
||||
|
||||
// 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;
|
||||
|
||||
// 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;
|
||||
|
||||
std::ofstream file("matrix_2.txt");
|
||||
for (int i = 0; i < N + 1; i++) {
|
||||
file << solution(i) << ' ';
|
||||
}
|
||||
file << std::endl;
|
||||
}
|
||||
|
||||
void Solver::Execute_Cubic(double val1, double val2) {
|
||||
// Локальная матрица жесткости (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 / 10.;
|
||||
|
||||
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) = -27 * 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) - 7. * B / 80.;
|
||||
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.;
|
||||
|
||||
// Локальный вектор нагрузки (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;
|
||||
|
||||
// Размер глобальной системы: для кубических элементов (4 узла на элемент, перекрытие по 2 узла)
|
||||
int ndof = 2 * N + 2;
|
||||
MatrixXd ansamb = MatrixXd::Zero(ndof, ndof);
|
||||
VectorXd global_load = VectorXd::Zero(ndof);
|
||||
|
||||
// АНСАМБЛИРОВАНИЕ
|
||||
for (int elem = 0; elem < N; ++elem) {
|
||||
int node_start = 2 * elem; // Начальный индекс для текущего элемента
|
||||
|
||||
// Добавляем локальную матрицу
|
||||
for (int i = 0; i < 4; ++i) {
|
||||
for (int j = 0; j < 4; ++j) {
|
||||
ansamb(node_start + i, node_start + j) += local(i, j);
|
||||
}
|
||||
}
|
||||
|
||||
// Добавляем локальный вектор нагрузки
|
||||
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;
|
||||
|
||||
// ГРАНИЧНЫЕ УСЛОВИЯ
|
||||
double u_left = val1; // u(1) = 5
|
||||
double u_right = val2; // u(6) = 15
|
||||
|
||||
ansamb.row(0).setZero();
|
||||
ansamb.col(0).setZero();
|
||||
ansamb(0, 0) = 1.0;
|
||||
global_load(0) = u_left;
|
||||
|
||||
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;
|
||||
|
||||
// Решение системы
|
||||
VectorXd solution = ansamb.fullPivLu().solve(global_load);
|
||||
std::cout << "\nSolution:" << std::endl;
|
||||
std::cout << solution << std::endl;
|
||||
|
||||
// Сохранение результатов (берем только значения функции в узлах, шаг 2)
|
||||
std::ofstream file("matrix_cubic.txt");
|
||||
for (int i = 0; i < ndof; i += 2) {
|
||||
file << solution(i) << ' ';
|
||||
}
|
||||
file << std::endl;
|
||||
}
|
||||
10
Solver.h
10
Solver.h
@@ -1,10 +0,0 @@
|
||||
#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_Linear(double value_1, double value_2);
|
||||
void Execute_Cubic(double value_1, double value_2);
|
||||
};
|
||||
256
graphics.ipynb
Normal file
256
graphics.ipynb
Normal file
@@ -0,0 +1,256 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "fda98006",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Solution of second-order linear ordinary differential equation"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "a4b21c72",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Input vars"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "6653253d",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"N = 20\n",
|
||||
"linear_file = f\"matrix_linear_{N}.txt\"\n",
|
||||
"cubic_file = f\"matrix_cubic_{N}.txt\""
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "781047cc",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## System cells"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "7fced95c",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def write_to_file(name: str, array):\n",
|
||||
" with open(f\"{name}\", 'w') as file:\n",
|
||||
" for element in array:\n",
|
||||
" file.write(f\"{element} \")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "d20bde93",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import numpy as np\n",
|
||||
"import matplotlib.pyplot as plt"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "8af07a56",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Solution of $5u'' + 4u' + 1 = 0, u'(0) = u(0), u(10) = 5$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "d0fe0703",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def u(x):\n",
|
||||
" return (9 * np.exp(8) * (x - 30) + 155 * np.exp(8 - 4 * x / 5) - 5 * (x + 1)) / (20 - 36 * np.exp(8))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "efac514a",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Linear element"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "18bd929b",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def show_plot_linear(filename: str, elements: int):\n",
|
||||
" with open(filename, 'r') as file:\n",
|
||||
" data_str = file.read()\n",
|
||||
"\n",
|
||||
" x = np.linspace(0, 10, elements + 1)\n",
|
||||
" y = np.fromstring(data_str, sep=' ')\n",
|
||||
" y_real = u(x)\n",
|
||||
"\n",
|
||||
" plt.plot(x, y, label=\"Linear element solution\", color='blue')\n",
|
||||
" plt.plot(x, y_real, label=\"Numeral solution\", color='black')\n",
|
||||
" plt.title(f\"Linear element, elements = {elements}\")\n",
|
||||
" plt.grid(True)\n",
|
||||
" plt.xlabel(\"x\")\n",
|
||||
" plt.ylabel(\"u(x)\")\n",
|
||||
" plt.legend()\n",
|
||||
" plt.savefig(f\"linear_{elements}.png\", dpi=300)\n",
|
||||
" plt.show()\n",
|
||||
"\n",
|
||||
" write_to_file(f\"linear_real_y_{elements}.txt\", y_real)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "d9a38740",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Cubic element"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "73525bc7",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def show_plot_cubic(filename: str, elements: int):\n",
|
||||
" with open(filename, 'r') as file:\n",
|
||||
" data_str = file.read()\n",
|
||||
"\n",
|
||||
" x = np.linspace(0, 10, 3 * elements + 1)\n",
|
||||
" y = np.fromstring(data_str, sep=' ')\n",
|
||||
" y_real = u(x)\n",
|
||||
"\n",
|
||||
" plt.plot(x, y, label=\"Cubic element solution\", color=\"red\")\n",
|
||||
" plt.plot(x, y_real, label=\"Numeral solution\", color='black')\n",
|
||||
" plt.title(f\"Cubic element, elements = {elements} \")\n",
|
||||
" plt.xlabel(\"x\")\n",
|
||||
" plt.ylabel(\"u(x)\")\n",
|
||||
" plt.grid(True)\n",
|
||||
" plt.legend()\n",
|
||||
" plt.savefig(f\"cubic_{elements}.png\", dpi=300)\n",
|
||||
" plt.show()\n",
|
||||
"\n",
|
||||
" write_to_file(f\"cubic_real_y_{elements}.txt\", y_real)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "3584baa4",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Main part"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "b8a772e3",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"show_plot_linear(linear_file, N)\n",
|
||||
"show_plot_cubic(cubic_file, N)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "22fe3de6",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Errors"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "31de1104",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def read_data_from_file(filename):\n",
|
||||
" with open(filename, 'r') as file:\n",
|
||||
" content = file.read().strip()\n",
|
||||
" data = np.array([float(x) for x in content.split()])\n",
|
||||
" return data"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "e0e9266d",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def show_error(program_file: str, analytical_file: str):\n",
|
||||
" # Считывание данных из файлов\n",
|
||||
" real = read_data_from_file(analytical_file)\n",
|
||||
" matrix = read_data_from_file(program_file)\n",
|
||||
" \n",
|
||||
" absolute_errors = np.abs(real - matrix)\n",
|
||||
" relative_errors = absolute_errors / (np.abs(real))\n",
|
||||
" relative_errors_percent = relative_errors * 100\n",
|
||||
"\n",
|
||||
" max_relative_error = np.max(relative_errors)\n",
|
||||
" max_relative_error_percent = np.max(relative_errors_percent)\n",
|
||||
" max_error_index = np.argmax(relative_errors)\n",
|
||||
"\n",
|
||||
" print(f\"\\nМаксимальная относительная погрешность: {max_relative_error:.6f} ({max_relative_error_percent:.2f}%)\")\n",
|
||||
" print(f\"Индекс точки с максимальной погрешностью: {max_error_index}\")\n",
|
||||
" print(f\"Значения в точке с максимальной погрешностью:\")\n",
|
||||
" print(f\" cubic_real: {real[max_error_index]}\")\n",
|
||||
" print(f\" matrix_cubic: {matrix[max_error_index]}\")\n",
|
||||
" print(f\" Абсолютная разность: {absolute_errors[max_error_index]:.6f}\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "89918171",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"show_error(linear_file, f\"linear_real_y_{N}.txt\")\n",
|
||||
"show_error(cubic_file, f\"cubic_real_y_{N}.txt\")"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.12.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
31
include/Solver.h
Normal file
31
include/Solver.h
Normal file
@@ -0,0 +1,31 @@
|
||||
// Особенности MSVC
|
||||
#define _SILENCE_EXPERIMENTAL_FILESYSTEM_DEPRECATION_WARNING
|
||||
|
||||
#pragma once
|
||||
#include <experimental/filesystem>
|
||||
using namespace std;
|
||||
using namespace std::experimental::filesystem;
|
||||
|
||||
class Solver {
|
||||
private:
|
||||
// Коэффициенты в ДУ
|
||||
double A, B, C, D;
|
||||
// Длина конечного элемента
|
||||
double L;
|
||||
// Количество конечных элементов
|
||||
int N;
|
||||
// Границы частного решения ДУ
|
||||
int upper, lower;
|
||||
public:
|
||||
Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u);
|
||||
void Execute_Linear(double value_1, double value_2);
|
||||
void Execute_Cubic(double value_1, double value_2);
|
||||
|
||||
bool check_path(string path) {
|
||||
return exists(path);
|
||||
}
|
||||
|
||||
void make_path(string path) {
|
||||
create_directory(path);
|
||||
}
|
||||
};
|
||||
18
src/MemMAPR-MKE.cpp
Normal file
18
src/MemMAPR-MKE.cpp
Normal file
@@ -0,0 +1,18 @@
|
||||
#include "Solver.h"
|
||||
#include "Header.h"
|
||||
#include <Eigen/Dense>
|
||||
#define A 5.
|
||||
#define B 4.
|
||||
#define C 0.
|
||||
#define D 1.
|
||||
|
||||
using namespace Eigen;
|
||||
int main() {
|
||||
std::cout << A << "u''" << " + " << B << "u'" << "+ " << C << "u + " << D << " = 0" << std::endl;
|
||||
Solver slv(A, B, C, D, 20, 0, 10);
|
||||
std::cout << "Linear element:";
|
||||
slv.Execute_Linear(0, 5);
|
||||
std::cout << "\nCubic element:";
|
||||
slv.Execute_Cubic(0, 5);
|
||||
return 0;
|
||||
}
|
||||
186
src/Solver.cpp
Normal file
186
src/Solver.cpp
Normal file
@@ -0,0 +1,186 @@
|
||||
#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) {
|
||||
if (_N < 1)
|
||||
throw std::runtime_error("N CAN BE OVER THAN 1!");
|
||||
|
||||
A = _A, B = _B, C = _C, D = _D, N = _N;
|
||||
upper = _u, lower = _l;
|
||||
L = (double)(upper - lower) / N;
|
||||
}
|
||||
|
||||
void Solver::Execute_Linear(double val1, double val2) {
|
||||
|
||||
// Локальная матрица жёсткости
|
||||
MatrixXd local = MatrixXd::Zero(2, 2);
|
||||
|
||||
// Локальный вектор нагрузки
|
||||
VectorXd local_load(2);
|
||||
|
||||
local(0, 0) = -A / L - B / 2. + C * L / 2.;
|
||||
local(0, 1) = A / L + B / 2. + C * L / 2.;
|
||||
local(1, 0) = A / L - B / 2. + C * L / 2.;
|
||||
local(1, 1) = -A / L + B / 2. + C * L / 2.;
|
||||
|
||||
local_load(0) = -D * L / 2.;
|
||||
local_load(1) = -D * L / 2.;
|
||||
|
||||
// Глобальная матрица жёсткости
|
||||
MatrixXd ansamb = MatrixXd::Zero(N + 2, N + 2);
|
||||
|
||||
// Глобальный вектор нагрузок
|
||||
VectorXd global_load = VectorXd::Zero(N + 2);
|
||||
|
||||
// Ансамблирование (с учётом смещения на 1)
|
||||
for (int elem = 0; elem < N; ++elem) {
|
||||
int node_i = elem + 1;
|
||||
int node_j = elem + 2;
|
||||
|
||||
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
|
||||
|
||||
// Boundary conditions
|
||||
double u_right = val2;
|
||||
|
||||
// 3rd type of boundary condition
|
||||
ansamb.row(0).setZero();
|
||||
ansamb(0, 0) = 1;
|
||||
ansamb(0, 1) = -1;
|
||||
global_load(0) = 0;
|
||||
ansamb(1, 1) -= A;
|
||||
|
||||
// 1st type of boundary condition
|
||||
for (int i = 0; i < global_load.size(); ++i) {
|
||||
global_load(i) = global_load(i) - u_right * ansamb(i, N + 1);
|
||||
}
|
||||
ansamb.row(N + 1).setZero();
|
||||
ansamb.col(N + 1).setZero();
|
||||
ansamb(N + 1, N + 1) = 1;
|
||||
global_load(N + 1) = 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
|
||||
|
||||
// Решение системы
|
||||
VectorXd solution = ansamb.fullPivLu().solve(global_load);
|
||||
std::cout << "\nSolution:" << std::endl;
|
||||
std::cout << solution << std::endl;
|
||||
|
||||
std::ofstream file("matrix_linear_" + std::to_string(N) + ".txt");
|
||||
for (int i = 1; i < solution.size(); i++) {
|
||||
file << solution(i) << ' ';
|
||||
}
|
||||
file << std::endl;
|
||||
}
|
||||
|
||||
void Solver::Execute_Cubic(double val1, double val2) {
|
||||
|
||||
int mat_dim = N * 3 + 2; // +2 для граничных узлов, как в линейном случае
|
||||
|
||||
// Локальная матрица жёсткости
|
||||
MatrixXd local = MatrixXd::Zero(4, 4);
|
||||
|
||||
// Локальный вектор нагрузки
|
||||
VectorXd local_load(4);
|
||||
|
||||
// Формирование локальной матрицы жёсткости
|
||||
local(0, 0) = -A * 37.0 / 10.0 / L + B * (-1.0) / 2.0 + C * 8. * L / 105.;
|
||||
local(0, 1) = -A * (-189.0) / 40.0 / L + B * 57.0 / 80.0 + C * 33. * L / 560.;
|
||||
local(0, 2) = -A * 27.0 / 20.0 / L + B * (-3.0) / 10.0 - C * 3. * L / 140.;
|
||||
local(0, 3) = -A * (-13.0) / 40.0 / L + B * 7.0 / 80.0 + C * 19. * L / 1680.;
|
||||
|
||||
local(1, 0) = -A * (-189.0) / 40.0 / L + B * (-57.0) / 80.0 + C * 33. * L / 560.;
|
||||
local(1, 1) = -A * 54.0 / 5.0 / L + C * 27. * L / 70.;
|
||||
local(1, 2) = -A * (-297.0) / 40.0 / L + B * 81.0 / 80.0 - C * 27. * L / 560.;
|
||||
local(1, 3) = -A * 27.0 / 20.0 / L + B * (-3.0) / 10.0 - C * 3. * L / 140.;
|
||||
|
||||
local(2, 0) = -A * 27.0 / 20.0 / L + B * 3.0 / 10.0 - C * 3. * L / 140.;
|
||||
local(2, 1) = -A * (-297.0) / 40.0 / L + B * (-81.0) / 80.0 - C * 27. * L / 560.;
|
||||
local(2, 2) = -A * 54.0 / 5.0 / L + C * 27. * L / 70.;
|
||||
local(2, 3) = -A * (-189.0) / 40.0 / L + B * 57.0 / 80.0 + C * 33. * L / 560.;
|
||||
|
||||
local(3, 0) = -A * (-13.0) / 40.0 / L + B * (-7.0) / 80.0 + C * 19. * L / 1680.;
|
||||
local(3, 1) = -A * 27.0 / 20.0 / L + B * 3.0 / 10.0 - C * 3. * L / 140.;
|
||||
local(3, 2) = -A * (-189.0) / 40.0 / L + B * (-57.0) / 80.0 + C * 33. * L / 560.;
|
||||
local(3, 3) = -A * 37.0 / 10.0 / L + B * 1.0 / 2.0 + C * 8. * L / 105.;
|
||||
|
||||
// Локальный вектор нагрузки
|
||||
local_load(0) = -D * L / 8.0;
|
||||
local_load(1) = -D * 3.0 * L / 8.0;
|
||||
local_load(2) = -D * 3.0 * L / 8.0;
|
||||
local_load(3) = -D * L / 8.0;
|
||||
|
||||
// Глобальные матрицы
|
||||
MatrixXd ansamb = MatrixXd::Zero(mat_dim, mat_dim);
|
||||
VectorXd global_load = VectorXd::Zero(mat_dim);
|
||||
|
||||
// Ансамблирование (со смещением на 1, как в линейной версии)
|
||||
for (int elem = 0; elem < N; ++elem) {
|
||||
int node_i = 1 + elem * 3; // смещение на 1
|
||||
for (int i = 0; i < 4; ++i) {
|
||||
for (int j = 0; j < 4; ++j) {
|
||||
ansamb(node_i + i, node_i + j) += local(i, j);
|
||||
}
|
||||
global_load(node_i + i) += local_load(i);
|
||||
}
|
||||
}
|
||||
|
||||
#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
|
||||
|
||||
// Граничные условия
|
||||
double u_right = val2;
|
||||
|
||||
// 3rd type of boundary condition
|
||||
ansamb.row(0).setZero();
|
||||
ansamb(0, 0) = 1;
|
||||
ansamb(0, 1) = -1;
|
||||
global_load(0) = 0;
|
||||
ansamb(1, 1) -= A;
|
||||
|
||||
// 1st type of boundary condition
|
||||
for (int i = 0; i < global_load.size(); ++i) {
|
||||
global_load(i) = global_load(i) - u_right * ansamb(i, mat_dim - 1);
|
||||
}
|
||||
ansamb.row(mat_dim - 1).setZero();
|
||||
ansamb.col(mat_dim - 1).setZero();
|
||||
ansamb(mat_dim - 1, mat_dim - 1) = 1;
|
||||
global_load(mat_dim - 1) = 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
|
||||
|
||||
// Решение системы
|
||||
VectorXd solution = ansamb.fullPivLu().solve(global_load);
|
||||
std::cout << "\nSolution:" << std::endl;
|
||||
std::cout << solution << std::endl;
|
||||
|
||||
std::ofstream file("matrix_cubic_" + std::to_string(N) + ".txt");
|
||||
for (int i = 1; i < solution.size(); i++) {
|
||||
file << solution(i) << ' ';
|
||||
}
|
||||
file << std::endl;
|
||||
}
|
||||
Reference in New Issue
Block a user