2014/10/07 by Herbert Egger, Fritz Kretzschmar, Egger, Herbert +7
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1410.1899
openalex publication_date 2014/10/07 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/01
The modeling and simulation of electromagnetic wave propagation is often\naccompanied by a restriction to bounded domains which requires the introduction\nof artificial boundaries. The corresponding boundary conditions should be\nchosen in order to minimize parasitic reflections. In this paper, we\ninvestigate a new type of transparent boundary condition for a discontinuous\nGalerkin Trefftz finite element method. The choice of a particular basis\nconsisting of polynomial plane waves allows us to split the electromagnetic\nfield into components with a well specified direction of propagation. The\nreflections at the artificial boundaries are then reduced by penalizing\ncomponents of the field incoming into the space-time domain of interest. We\nformally introduce this concept, discuss its realization within the\ndiscontinuous Galerkin framework, and demonstrate the performance of the\nresulting approximations by numerical tests. A comparison with first order\nabsorbing boundary conditions, that are frequently used in practice, is made.\nFor a proper choice of basis functions, we observe spectral convergence in our\nnumerical test and an overall dissipative behavior for which we also give some\ntheoretical explanation.\n