A Trefftz Discontinuous Galerkin method for time-harmonic waves with a generalized impedance boundary condition. Issue 3 (17th February 2020)

• Record Type: Journal Article
• Authors: Kapita, Shelvean; Monk, Peter; Selgas, Virginia
• Is Part Of: Applicable analysis. Volume 99:Issue 3(2020)
• Page Start: 379
• Page End: 406
• Publication Date: 2020-02-17
• Subjects: Yongzhi Xu; Helmholtz equation -- Trefftz -- discontinuous Galerkin -- generalized impedance boundary condition -- error estimate -- artificial boundary condition; 65N30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1498965
• Languages: English
• ISSNs: 0003-6811

Abstract

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.