PDE solver

This C++ program provides a solver for the steady-state 2D heat equation with Dirichlet boundary conditions. It offers two methods for solving the equation: Jacobi and Gauss-Seidel.

Table of Contents

• Overview
• Building

Overview

This project implements a solver for the 2D Poisson steady-state heat equation using C++. It provides Dirichlet boundary conditions and two iterative methods for solving the equation: Jacobi and Gauss-Seidel.

Reference: https://gitlab.lrz.de/tum-i05/public/advprog-project-ideas/-/blob/master/pde-solver/pde-solver.md?ref_type=heads

Project Structure

• src/: Contains the main source files of the project.
  • functions/: Directory for function implementations relevant to the solver.
  • main.cpp
• tests/: Contains unit tests for the solver.
  • jacobiTest.cpp: Unit tests for the Jacobi method implementation.
• build/: Directory for build files
• .gitignore: Git ignore file to exclude specific files and directories.
• README.md.

Building the Project

To build the project, follow these steps:

1. Ensure CMake is installed on your system.

2. Navigate to the root directory of the project.

3. Run the following commands:

   mkdir build
   cd build
   cmake ..
   make

Running the Solver

After building the project, you can run the solver by executing the binary created in the build/ directory. Follow these steps:

1. Navigate to the build/ directory.

2. Execute the solver binary. The command may vary depending on the name of the binary, but typically it will be something like:

   ./src/PDEsolver

3. The program will ask you to provide the path to a file that contains the parameters to run the solver and the boundary conditions. Provide the path to your file or modify and use the default one:

   ../default.csv

   which follows the required syntax standard for the parameters definition:

   rows,50
   columns,50
   method,1
   tolerance,0.05
   maxIterations,5000
   outputFile,default_matrix.csv
   topBoundary,sinusoidal,5
   bottomBoundary,constant,10
   leftBoundary,constant,2
   rightBoundary,sinusoidal,2

Testing

The project includes unit tests, particularly for the Jacobi iterative method. To run the tests, navigate to the build/ directory and execute:

./src/PDEsolver --test

Performance

For detailed information on the performance analysis and optimization strategies applied to this project, please refer to the Performance Analysis and Optimization Report.