Well-posed boundary integral equation formulations and nyström discretizations for the solution of Helmholtz transmission problems in two-dimensional lipschitz domains

Document Type

Article

Publication Date

1-1-2016

Abstract

We present a comparison among the performance of solvers based on Nyström discretizations of several well-posed boundary integral equation formulations of Helmholtz transmission problems in two-dimensional Lipschitz domains. Specifically, we focus on the following four classes of boundary integral formulations of Helmholtz transmission problems: (1) the classical first kind integral equations for transmission problems [13], (2) the classical second kind integral equations for transmission problems [25], (3) the single integral equation formulations [21], and (4) certain direct counterparts of recently introduced generalized combined source integral equations [4, 5]. The former two formulations were the only formulations whose wellposedness in Lipschitz domains was rigorously established [13, 36]. We establish the well-posedness of the latter two formulations in appropriate functional spaces of boundary traces of solutions of transmission Helmholtz problems in Lipschitz domains. We give ample numerical evidence that Nyström solvers based on formulations (3) and (4) are computationally more advantageous than solvers based on the classical formulations (1) and (2), especially in the case of high-contrast transmission problems at high frequencies.

Identifier

84994807350 (Scopus)

Publication Title

Journal of Integral Equations and Applications

External Full Text Location

https://doi.org/10.1216/JIE-2016-28-3-395

ISSN

08973962

First Page

395

Last Page

440

Issue

3

Volume

28

Grant

1312169

Fund Ref

National Science Foundation

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