SCHJonathan / Discrete-Harmonic-Functions-and-Dirichlet-s-Relaxation-Method

This project is based on an undergraduate research project at the Illinois Geometry Lab and directed by A.J. Hildebrand. Reviewed and published in Wolfram Demonstrations Project website.

Discrete Harmonic Function and Dirichlet's Relaxation Process

The goal of this project is to create interactive Mathematica-based visualizations of interesting mathematical topics for use in instruction and outreach activities. In particular, this project focuses on visualizations illustrating discretized harmonic functions, Dirichlet problem, Dirichlet energy, and Dirichlet's relaxation process. This project is reviewed and published at Wolfram Demonstrations Project. This project is based on an undergraduate research project at the Illinois Geometry Lab and directed by A.J. Hildebrand.

Getting Started

These instructions will get you a copy of the project up and running on your local machine for development and testing purposes. In this repository, I include two different versions of the same software (DiscreteHarmonicFunctionsDemonstrations.nb and DiscreteHarmonicFunctionsDemonstrations.m). DiscreteHarmonicFunctionsDemonstrations.m is simply the source code of the DiscreteHarmonicFunctionsDemonstrations.nb.

Prerequisites

• This project is based on Mathematica programming language, which requires to install the software and run the program in a notebook format. Once downloaded, you can simply run the program by double clicking the DiscreteHarmonicFunctionsDemonstrations.nb file. If you double click this file without Mathematcia installed, it will show up garbage code but you can still view the source code by double clicking the DiscreteHarmonicFunctionsDemonstrations.m file.

• (Optional) Good text editor.

Installing

1. Download Mathematica

2. Open up terminal and direct to desire directory to clone this project.

   • (optional) Or you can click the "Clone or Download" button in upper right corner and select "Download ZIP" to download this repository into your desire directory. Then, upzip downloaded file and skip tp step 5.

3. In that directory, clone this repository into your own machine by typing in the following command in termial:

   git clone https://github.com/Jonathan-UIUC/Discrete-Harmonic-Functions-and-Dirichlet-s-Relaxation-Method.git
   

4. A new folder should appear in that directory and you can open up the folder by typing the following command in termial:

   open Discrete-Harmonic-Functions-and-Dirichlet-s-Relaxation-Method
   

5. double click the file DiscreteHarmonicFunctionsDemonstrations.nb and enjoy the demosntration. :)

Screen Shoots

Contributing

Please read CONTRIBUTING.md for details on our code of conduct, and the process for submitting pull requests to us.

Reference

see Wolfram Demonstrations Project.

Authors

• Yuheng Chang

• A.J. Hildebrand (Faculty Mentor)

License

This project is licensed under the MIT License - see the LICENSE.md file for details