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);