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

Fatih Ecevit, Akash Anand, Yassine Boubendir

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number1
JournalJournal of Scientific Computing
Volume83
Issue number1
DOIs
StatePublished - Apr 1 2020

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Galerkin boundary element method
  • High-frequency
  • Multiple-scattering

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