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Journal of Scientific Computing

Erschienen in:

01.04.2020

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

verfasst von: Fatih Ecevit, Akash Anand, Yassine Boubendir

Erschienen in: Journal of Scientific Computing | Ausgabe 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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Titel: Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems
verfasst von: Fatih Ecevit
Akash Anand
Yassine Boubendir
Publikationsdatum: 01.04.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01189-x

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