DG Maxwell

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Introduction

This projects aims at developing a fast Maxwell's Equation solver using using the discontinuous Galerkin method. As first steps to develop this solver, we are developing a library which allows us to solve the 1D wave equation and the 2D wave equation using discontinuous Galerkin method.

1D Wave equation

The 1D wave equation solver is aimed at finding the time evolution of the 1D wave equation using the discontinuous Galerkin method. The 1D wave equation is given by the equation:

where,

where, is a number which denotes the wave speed.

2D Wave Equation Solver

The 2D wave equation solver is aimed at finding the time evolution of the 2D wave equation using the discontinuous Galerkin method. The 2D wave equation is given by the equation:

where,

where, and denotes the component of the wave speed in the and direction respectively.

Through the development of the 2D wave equation solver, the code and the algorithms developed here will help in creating the 2D Maxwell's equation solver. Currently the 2D wave equation solver will focus on solving the wave equation in a rectangular domain in the plane, with periodic boundary conditions.

Dependencies

• matplotlib
• numpy
• arrayfire
• gmshtranslate
• texlive
• h5py
• tqdm
• scipy
• pytest
• pytest-cov
• coveralls
• python-coveralls

Documentation

The documenation for the project can be generated using sphinx from the docs directory. You may read the instructions here.

Unit tests

The unit tests are located in the code/tests directory.

Dependencies

• pytest

Running Unit Tests

To run the unit tests, enter the following commands

$ cd path/to/the/DG_Maxwell/repo
$ pytest

• The parameters of the simulation are stored in params.py in the app folder, These can be changed accordingly.

• To obtain the movie of the 1D wave advection, run post_processing.py file after the simulation. The movie will be created automatically and stored in results folder.

Maintainers

• Aman Abhishek Tiwari - [email protected]
• Balavarun P - [email protected]
• Manichandra Morumpudi - [email protected]