dl-wuhee / finite-difference-method

A Finite Difference Method Engine in C++

Finite-Difference-Method

A Finite Difference Method Engine in C++

This repository hosts a small library/engine for solving spacial differential equations using the finite difference method. This was created as a fun way to explore numerical methods as a stepping stone for the Finite Elements Method. Feel free to use this code as an example of how to numerically solve partial differential equations.

How it Works

Spacial variables such as the object length, conductivity, and step size across the mesh are kept in the Mesh class. An example of filling out relevant Mesh information is showen below.

Mesh1D mesh;

mesh.spacial_length = 10;

mesh.spacial_step_size = 1;

mesh.thermal_conductivity = 0.01;

The boundary condition is represented by a function that takes two parameters: x and y. The boundary condition can be changed by changing the equation inside. For example, a periodic boundary condition can be represented by

double BC(double x, int y)
{
	return sin(x)*cos(y);
}

The boundary condition also belongs to the mesh.

mesh.DirchletBoundaryEquation = BC;

Engine1D engine;

engine.StartSimulation(mesh);