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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

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.