Heterogeneous Multiscale Methods for Maxwell's equations

The following software contain implementations of the heterogeneous multiscale method for linear Maxwell's equations based on the finite element library deal.II in C++. It was developed as part of the Master's thesis of Bernhard Maier and the proceeding paper Heterogeneous Multiscale Method for Maxwell's equations.

An extension to dispersive systems was considered (within project A3) in the doctoral thesis Numerical homogenization of time-dependent Maxwell's equations with dispersion effects of Philip Freese, see also the paper The heterogeneous multiscale method for dispersive Maxwell systems.

For details on the derivation and error analysis of these schemes, have a look at the respective publications.

Requirements

To run simulations, deal.II (last checked for version 9.0.0, respectively 9.1.1) has to be installed with MPI, Trilinos and p4est. Further details of the implementation can be found in the corresponding README files and in the documentation.

Access to software

The general software for the non-dispersive system can be downloaded here HMM-Maxwell.tar.gz (~64kb)

The config files for the model problem considered

• in the abstract for the 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation can be found here https://www.waves.kit.edu/downloads/software/hmm/config_waves19.ini.
• in Heterogeneous Multiscale Method for Maxwell's equations can be found here https://www.waves.kit.edu/downloads/software/hmm/configs_HMM_SIAM_MMS.tar.gz.

The codes for the dispersive system can be accessed here https://www.doi.org/10.5445/IR/1000129217.

We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173.