Well-conditioned boundary integral equation formulations and nyström discretizations for the solution of Helmholtz problems with impedance boundary conditions in two-dimensional Lipschitz domains

Document Type

Article

Publication Date

1-1-2017

Abstract

We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helmholtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of classical impedance boundary conditions, as well as that of transmission impedance conditions wherein the impedances are certain coercive operators. The latter type of problem is instrumental in the speed up of the convergence of Domain Decomposition Methods for Helmholtz problems. Our regularized formulations use as unknowns the Dirichlet traces of the solution on the boundary of the domain. Taking advantage of the increased regularity of the unknowns in our formulations, we show through a variety of numerical results that a graded-mesh based Nyström discretization of these regularized formulations leads to efficient and accurate solutions of interior and exterior Helmholtz problems with impedance boundary conditions.

Identifier

85028679978 (Scopus)

Publication Title

Journal of Integral Equations and Applications

External Full Text Location

https://doi.org/10.1216/JIE-2017-29-3-441

ISSN

08973962

First Page

441

Last Page

472

Issue

3

Volume

29

Grant

DMS-1312169

Fund Ref

National Science Foundation

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