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Journal of Scientific Computing

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01-04-2020

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

Authors: Fatih Ecevit, Akash Anand, Yassine Boubendir

Published in: Journal of Scientific Computing | Issue 1/2020

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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 $\mathcal {O}(k^{\epsilon })$ (for any $\epsilon >0$) with increasing wavenumber k to attain frequency-independent error tolerances. We support our theoretical developments by a variety of numerical implementations.

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Title: Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems
Authors: Fatih Ecevit
Akash Anand
Yassine Boubendir
Publication date: 01-04-2020
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2020
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01189-x

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