Solve a 2D Poisson partial differential equation by finite differences and using OpenMP.
The implemented program is based on the pseudocode of the book (Burden and Faires, 2010). The solution for the PDE represented below:
where the subtitles numerico ( is the numerical solution), and analitico ( is the analytical solution). The average uncertainty of the resolution is in the ninth decimal place.
The code in c solves the Poisson elliptical P.D.E by calculating the matrix that approximates the solution to the P.D.E. The steps to calculate the matrix are illustrated above.
This program serves to learn the methods of gauss seidel and finite differences, as well as to solve any elliptic P.D.E category with the appropriate boundary condition. Boundary conditions and start function are shown at the beginning of the code and can be changed as needed. 😃
The code using the shared memory API has a chunk size = 80, just for safety and to avoid possible future errors, since later we define the chunk size = multiple of the number of threads.
To compile the code you need any compiler that has the OpenMP shared memory API (compilers list: https://www.openmp.org/resources/openmp-compilers-tools/), however it is recommended to use GNU compiler, because some specific optimization flags I used can only be applied with this compiler.
To compile the code in serial using the GNU compiler do:
gcc PDE_MM_SerialCode.c -lmand run:
./a.outTo compile the code in parallel using the GNU compiler do:
gcc -fopenmp -o prg.x PDE_MM_OpenMPCode.c -lmexport the number of threads:
export OMP_NUM_THREADS=number of threadsand run the program at the end:
./prg.x- OpenMP-4.0 - Documentation OpenMP version 4.0
- OpenMP-4.5 - Documentation OpenMP version 4.5
Reviews and suggestions feel free to send me:
e-mail: marcosmatheusdepaivasilva@gmail.com
LinkedIn: https://www.linkedin.com/in/marcos-matheus-silva-089699b3/ 🤗
Marcos Matheus de Paiva Silva
This project is licensed under the MIT License - see the LICENSE file for details