thomasthelen/finite-difference-method

A Finite Difference Method Engine in C++

FDM

FDM is a C++ source library that exposes an engine for running the method of Finite Elements across one dimension. This is mostly a personal exploration of The Finite Difference Method, CUDA, and Python Bindings.

Using

To use the engine, git clone the repository and include the required headers in your source file. Examples are given in the examples directory.

Building

To build, run cmake .. and cmake --build . from the build/ directory.

Source

The project has a few directories to separate various parts of the project, detailed below

• build/: Contains the build output
• examples: Examples of how the library can be used
• src: The source code for the engine

Overview

The Mesh struct manages information about the object being simulated over. There's an associated Mesh class for each dimension. For example, one dimensional simulations should use 1DMesh.

The Engine class parses information from associated mesh and is responsible for encapsulating the routines for the Finite Difference Method.

Creating Simulations

A successful simulation will have both a Mesh and an Engine class instantiated.

The mesh must have the following defined,

mesh.spatial_length = 10;
mesh.spatial_step_size = 1;
mesh.thermal_conductivity = 0.01;
mesh.DirchletBoundaryEquation = BC;
mesh.InitialDistribution = InitialRodDistribution;

The boundary condition must be a function with the signature

double BoundaryCondition(double x, int time)

For example,

double BoundaryCondition(double x, int time)
{
	return 15*x+t/2;
}

The initial distribution method provides an interface to defining the temperature along the object and must have a signature of

double TempDistribution(double position)

For example, a function that defines the temperature as a constant 50 between the boundary points...

double TempDistribution(double position) {
	return 10;
}

To run, call StartSimulation on the engine object and pass it the mesh object.

Engine engine;
engine.StartSimulation(int time_length, int time_step, Mesh1D& mesh);

finite-difference-method's Issues

Remove `this` References

The cpp file has a million references to this when it isn't needed. Remove them

Optimize Vectors

I've seen a few cases where the size of the vector is known before use. Use .reserve to stop re-allocations.

Treat Warnings as Errors

Enable treating warnings as errors, and fix all the warnings.

Get Rid of Raw Function Pointers

Class Mesh2D has several function pointers that need to be replaced with std::function.

Transition to CMake

Let's make this buildable. Move over to CMake

2D Heat diffusion example with Neuman conditions (flux)

Hello,
Could it be possible to have and example of 2D heat diffusion, if possible with heat flux conditions ?
Thank you very much !