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arXiv · 1709.04948

A Trefftz Discontinuous Galerkin Method for Time Harmonic Waves with Generalized Impedance Boundary Conditions

Shelvean Kapita·Peter Monk·Virginia Selgas
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Abstract

We show how a Trefftz Discontinuous Galerkin (TDG) method for the displacement form of the Helmholtz equation can be used to approximate problems having a generalized impedance boundary condition (GIBC) involving surface derivatives of the solution. Such boundary conditions arise naturally when modeling scattering from a scatterer with a thin coating. The thin coating can then be approximated by a GIBC. A second place GIBCs arise is as higher order absorbing boundary conditions. This paper also covers both cases. Because the TDG scheme has discontinuous elements, we propose to couple it to a surface discretization of the GIBC using continuous finite elements. We prove convergence of the resulting scheme and demonstrate it with two numerical examples.

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Shelvean Kapita, Peter Monk, Virginia Selgas. 2017-09-14. A Trefftz Discontinuous Galerkin Method for Time Harmonic Waves with Generalized Impedance Boundary Conditions. https://arxiv.org/abs/1709.04948

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