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We show how a Trefftz Discontinuous Galerkin (TDG) method for thedisplacement form of the Helmholtz equation can be used to approximate problemshaving a generalized impedance boundary condition (GIBC) involving surfacederivatives of the solution. Such boundary conditions arise naturally whenmodeling scattering from a scatterer with a thin coating. The thin coating canthen be approximated by a GIBC. A second place GIBCs arise is as higher orderabsorbing boundary conditions. This paper also covers both cases. Because theTDG scheme has discontinuous elements, we propose to couple it to a surfacediscretization of the GIBC using continuous finite elements. We proveconvergence of the resulting scheme and demonstrate it with two numericalexamples.

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