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

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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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Authors and Affiliations

  1. Department of Mathematics, Boğaziçi University, Bebek TR, 34342, Istanbul, Turkey

    Fatih Ecevit

  2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, 327 Faculty Building, Kanpur, UP, 208016, India

    Akash Anand

  3. Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102, USA

    Yassine Boubendir

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  1. Fatih Ecevit
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  2. Akash Anand
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  3. Yassine Boubendir
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Correspondence to Fatih Ecevit.

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F. Ecevit’s work was supported by The Scientific and Technological Research Council of Turkey through grant number TÜBİTAK-1001-117F056. A. Anand gratefully acknowledges support from IITK-ISRO Space Technology Cell through contract No. STC/MATH/2014100. Y. Boubendir’s work was supported by the NSF through Grant DMS-1720014.

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Ecevit, F., Anand, A. & Boubendir, Y. Galerkin Boundary Element Methods for High-Frequency Multiple-Scattering Problems. J Sci Comput 83, 1 (2020). https://doi.org/10.1007/s10915-020-01189-x

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

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