Electromagnetics - Modelling, Simulation, Control and Industrial Applications - Abstract

Schnepp, Sascha

Approaches to time-domain electromagnetics with the discontinuous Galerkin method

Two DG approaches to the simulation of time-domain electromagnetics are outlined.
First, a rather classical discretization of Maxwell's equations in space employing hexahedral meshes and a tensor product basis is presented. The formulation and the resulting implementation is very flexible and allows for high level hanging nodes as well as directionally independent orders of the tensor product space in each element. The combination of these features enables anisotropic mesh refinement with respect to the mesh step size $h$ and the approximation order $p$. A modified error estimate based on the idea of reference solutions citeDemkowicz1 is introduced, which is computationally much more efficient citeSchnepp:2013vv.
Second, a novel space-time DG Trefftz method is presented. In a Trefftz-type finite element method the basis functions are required to exactly fulfill the underlying PDE citeJirousek:1997uc. This characteristic feature is known to yield very good approximation properties. The basic formulation of the method will be presented along with first numerical results citeKretzschmar:2013wt. beginthebibliography9 bibitemDemkowicz1 L. Demkowicz, Computing with HP-Adaptive Finite Elements: Volume 1: One and Two Dimensional Elliptic and Maxwell Problems, Chapman & Hall/CRC, 2007. bibitemSchnepp:2013vv S. M. Schnepp, Error-Driven Dynamical hp-Meshes for the Discontinuous Galerkin Method in Time-Domain, arXiv (submitted to IEEE Transactions on Antennas & Propagation). http://arxiv.org/abs/1301.6562 bibitemJirousek:1997uc J Jirousek A and Zielinski, emphSurvey of Trefftz-type element formulations, Computers & structures 63(2) pp 225--242, 1997 bibitemKretzschmar:2013wt F. Kretzschmar, S. M. Schnepp, I. Tsukerman, T. Weiland, Discontinuous Galerkin Methods with Trefftz Approximation, arXiv (submitted to Journal of Computational Physics). http://arxiv.org/abs/1302.6459 endthebibliography Acknowledgments:
Sascha M. Schnepp acknowledges the support of the `Alexander von Humboldt-Foundation' through a `Feodor Lynen Research Fellowship'.