https://github.com/mm318/fem-solver-2d-poisson

Finite Element Method solver for 2D Poisson problems
https://github.com/mm318/fem-solver-2d-poisson

finite-element-method finite-elements poisson-equation pure-c visualization

Last synced: 29 days ago
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Finite Element Method solver for 2D Poisson problems

• Host: GitHub
• URL: https://github.com/mm318/fem-solver-2d-poisson
• Owner: mm318
• Created: 2023-03-27T23:06:48.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-08-27T22:18:35.000Z (over 1 year ago)
• Last Synced: 2023-08-27T23:32:18.470Z (over 1 year ago)
• Topics: finite-element-method, finite-elements, poisson-equation, pure-c, visualization
• Language: C
• Homepage:
• Size: 1.64 MB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Finite Element Method Solver for 2D Poisson Problems

![build](https://github.com/mm318/fem-solver-2d-poisson/actions/workflows/build.yml/badge.svg)

This package takes a .poly file that defines the problem boundary

(see [here](https://www.cs.cmu.edu/~quake/triangle.poly.html) to understand the file format)

and solves the 2D screened Poisson equation:

```math

\Delta u(x,y) - u(x,y) = -{x^2 + y^2 - 4 \over 250000}

```

subject to the Dirichlet boundary condition:

```math

u(x,y) = {x^2 + y^2 \over 250000}

```

(The problem can be modified by editing `prob_def.c`)

This was for a university project in 2011.

## Usage

### Installation

```bash

# in /

git clone https://github.com/mm318/fem-solver-2d-poisson.git

```

### Build

```bash

# from /

mkdir build

cd build

cmake ../fem-solver-2d-poisson

make

```

### Run

Usage:

```text

FEM_Solver <.poly file>

```

Example:

```bash

# from /build/

cd bin  # current working directory needs to have the plstnd5.fnt and plxtnd5.fnt files

./FEM_Solver bicycle_seat # exclude the .poly extension

```

Resulting mesh:  

![bicycle_seat mesh](bin/bicycle_seat_example_mesh.png "bicycle_seat mesh")

Resulting solution:  

![bicycle_seat solution](bin/bicycle_seat_example.png "bicycle_seat solution")  

![bicycle_seat solution plot](bin/bicycle_seat_example_plot.png "bicycle_seat solution plot")

## Requirements

Tested on Ubuntu 20.04 and Ubuntu 22.04.

## Dependencies

- [FEM2D_POISSON](https://people.math.sc.edu/Bu/rkardt/cpp_src/fem2d_poisson_cg/fem2d_poisson_cg.html) - LGPL

- [Triangle](https://www.cs.cmu.edu/~quake/triangle.html) - Non-commercial use

- [PLplot](https://plplot.sourceforge.net/) - LGPL

- [libgd](https://libgd.github.io/) - BSD-like

- [libpng](http://www.libpng.org/pub/png/libpng.html) - The zlib/libpng License

- [zlib](https://zlib.net/) - The zlib/libpng License