Numerical solver of Laplace's equation

This repository contains a small C code that implements a finite difference solver of Laplace's equation. It also provides a multi-threaded version of the algorithm. To define a boundary conditions, one must create a function like the one showed below.

Running

To run the code, simply clone this repository and edit the main.c file to match the desired problem.

$ git clone https://github.com/TheNiceGuy/laplace
$ mkdir -p laplace/build && cd laplace/build
$ cmake .. && make
$ ./laplace

The matrix will be written in stderr, thus you can save it to a file using simple IO redirection.

$ ./laplace 2> data.csv

A simple script is provided in the scripts folder that can plot the data using matplotlib. The following command will create an image file.

$ ./graph.py data.csv

The following command will show the data directly.

$ ./graph.py data.csv --show

Examples

struct bound* boundaries(struct bound* bound, struct rect* pos) {
    double x = pos->x;
    double y = pos->y;

    if(x < 16 && y <= 0) {
        bound->value =  150;
        bound->cond  = DIRICHLET;
    } else if(48 <= x && x <= 64 && y <= 0) {
        bound->value = -150;
        bound->cond  = DIRICHLET;
    } else if(16 <= x && x< 48 && (y < 12 || y >= 36)) {
        bound->value = 0;
        bound->cond  = NEUMANN;
    } else {
        bound->value = 0;
        bound->cond  = NONE;
    }

    return bound;
}

struct bound* boundaries(struct bound* bound, struct rect* pos) {
    double x = pos->x;
    double y = pos->y;

    if(x < 16 && y <= 0) {
        bound->value =  150;
        bound->cond  = DIRICHLET;
    } else if(48 <= x && x <= 64 && y <= 0) {
        bound->value = -150;
        bound->cond  = DIRICHLET;
    } else if(16 <= x && x< 48 && (y < 12 || y >= 36)) {
        bound->value = 0;
        bound->cond  = NEUMANN;
    } else if(10 <= x && x < 20 && 25 <= y && y < 30) {
        bound->value = 0;
        bound->cond  = NEUMANN;
    } else if(30 <= x && x < 55 && 15 <= y && y < 18) {
        bound->value = 60;
        bound->cond  = DIRICHLET;
    } else {
        bound->value = 0;
        bound->cond  = NONE;
    }

    return bound;
}