Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems

Document Type

Article

Publication Date

4-1-2020

Abstract

We consider high-frequency multiple-scattering problems in the exterior of two-dimensional smooth scatterers consisting of finitely many compact, disjoint, and strictly convex obstacles. To deal with this problem, we propose Galerkin boundary element methods, namely the frequency-adapted Galerkin boundary element methods and Galerkin boundary element methods generated using frequency-dependent changes of variables. For both of these new algorithms, in connection with each multiple-scattering iterate, we show that the number of degrees of freedom needs to increase as O(kϵ) (for any ϵ> 0) with increasing wavenumber k to attain frequency-independent error tolerances. We support our theoretical developments by a variety of numerical implementations.

Identifier

85082119789 (Scopus)

Publication Title

Journal of Scientific Computing

External Full Text Location

https://doi.org/10.1007/s10915-020-01189-x

e-ISSN

15737691

ISSN

08857474

Issue

1

Volume

83

Grant

DMS-1720014

Fund Ref

National Sleep Foundation

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