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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.
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.
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.
The documenation for the project can be generated using sphinx
from the docs directory. You may read the instructions
here.
The unit tests are located in the code/tests directory.
To run the unit tests, enter the following commands
$ cd path/to/the/DG_Maxwell/repo
$ pytest --verbose -r P --color=yes --cov dg_maxwell
-
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.pyfile after the simulation. The movie will be created automatically and stored inresultsfolder.
- Aman Abhishek Tiwari -
- Balavarun P -
- Manichandra Morumpudi -