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Transparent boundary conditions for a discontinuous Galerkin Trefftz method

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  • Egger, Herbert
  • Kretzschmar, Fritz
  • Schnepp, Sascha M.
  • Tsukerman, Igor
  • Weiland, Thomas

Abstract

The modeling and simulation of electromagnetic wave propagation is often accompanied by a restriction to bounded domains which requires the introduction of artificial boundaries. The corresponding boundary conditions should be chosen in order to minimize parasitic reflections. In this paper, we investigate a new type of transparent boundary condition for a discontinuous Galerkin Trefftz finite element method. The choice of a particular basis consisting of polynomial plane waves allows us to split the electromagnetic field into components with a well specified direction of propagation. The reflections at the artificial boundaries are then reduced by penalizing components of the field incoming into the space–time domain of interest. We formally introduce this concept, discuss its realization within the discontinuous Galerkin framework, and demonstrate the performance of the resulting approximations by numerical tests. A comparison with first order absorbing boundary conditions, that are frequently used in practice, is made. For a proper choice of basis functions, we observe spectral convergence in our numerical test and an overall dissipative behavior for which we also give some theoretical explanation.

Suggested Citation

  • Egger, Herbert & Kretzschmar, Fritz & Schnepp, Sascha M. & Tsukerman, Igor & Weiland, Thomas, 2015. "Transparent boundary conditions for a discontinuous Galerkin Trefftz method," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 42-55.
    • Handle: RePEc:eee:apmaco:v:267:y:2015:i:c:p:42-55
    DOI: 10.1016/j.amc.2015.06.026
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    Cited by:

    1. Yuan, Long & Gong, Wenxiu, 2023. "A space–time Trefftz DG scheme for the time-dependent Maxwell equations in anisotropic media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 445-469.

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