Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 3
183
Views
0
CrossRef citations to date
0
Altmetric
Articles

A Trefftz Discontinuous Galerkin method for time-harmonic waves with a generalized impedance boundary condition

, &
Pages 379-406 | Received 26 Jul 2017, Accepted 28 Feb 2018, Published online: 19 Jul 2018
 

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.

COMMUNICATED BY:

AMS SUBJECT CLASSIFICATION:

Acknowledgements

Peter Monk and Shelvean Kapita acknowledge the support of the IMA, University of Minnesota during the special year ‘Mathematics and Optics’.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Peter Monk is partially supported by NSF [grant number: DMS-1619904]. The research of Virginia Selgas is partially supported by MCI project number [MTM2013-43671-P].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.