Alternating Direction Implicit method for Maxwell equations

Space discretization with a discontinuous Galerkin method

The following code contains an implementation of a fully discrete discontinuous Galerkin alternating direction implicit discretization for Maxwell equations developed and analyzed within the project A4.

For information about these schemes have a look at the paper Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems by Jonas Köhler and Marlis Hochbruck.

Further information can be found in the doctoral thesis The Peaceman–Rachford ADI-dG method for linear wave-type problems of Jonas Köhler.

Access to software

The code can be accessed via this link. It is written in C++, based on the finite element library deal.II. Further details about the requirements can be found in the Readme file.

Space discretization with the Yee grid

This is the source code for the numerical example in the publication Analysis of a Peaceman–Rachford ADI scheme for Maxwell equations in heterogenous media by Konstantin Zerulla and Tobias Jahnke. In this joint work of projects A4 and A7, we consider the Maxwell equations on a cuboid with discontinuous material parameters. These discontinuities reduce the regularity of the solution, and as a consequence, the time-discretization with the ADI method converges only with order 3/2 instead of 2, as predicted by our analysis. For the space discretization we have used the classical Yee grid.

The code was written in MATLAB by Tobias Jahnke with modifications by Konstantin Zerulla.