Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects

Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects

Year:    2018

Communications in Computational Physics, Vol. 23 (2018), Iss. 1 : pp. 264–295

Abstract

We consider acoustic scattering of time-harmonic waves at objects composed of several homogeneous parts. Some of those may be impenetrable, giving rise to Dirichlet boundary conditions on their surfaces. We start from the recent second-kind boundary integral approach of [X. Claeys, and R. Hiptmair, and E. Spindler. A second-kind Galerkin boundary element method for scattering at composite objects. BIT Numerical Mathematics, 55(1):33-57, 2015] for pure transmission problems and extend it to settings with essential boundary conditions. Based on so-called global multi-potentials, we derive variational second-kind boundary integral equations posed in L2(Σ), where Σ denotes the union of material interfaces. To suppress spurious resonances, we introduce a combined-field version (CFIE) of our new method.
Thorough numerical tests highlight the low and mesh-independent condition numbers of Galerkin matrices obtained with discontinuous piecewise polynomial boundary element spaces. They also confirm competitive accuracy of the numerical solution in comparison with the widely used first-kind single-trace approach.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2016-0171

Communications in Computational Physics, Vol. 23 (2018), Iss. 1 : pp. 264–295

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:    Acoustic scattering second-kind boundary integral equations Galerkin boundary element methods.

  1. Second kind boundary integral equation for multi-subdomain diffusion problems

    Claeys, X. | Hiptmair, R. | Spindler, E.

    Advances in Computational Mathematics, Vol. 43 (2017), Iss. 5 P.1075

    https://doi.org/10.1007/s10444-017-9517-0 [Citations: 6]
  2. Second-kind boundary integral equations for electromagnetic scattering at composite objects

    Claeys, Xavier | Hiptmair, Ralf | Spindler, Elke

    Computers & Mathematics with Applications, Vol. 74 (2017), Iss. 11 P.2650

    https://doi.org/10.1016/j.camwa.2017.08.014 [Citations: 3]
  3. A fast preconditioned iterative method for the electromagnetic scattering by multiple cavities with high wave numbers

    Zhao, Meiling | Zhu, Na

    Journal of Computational Physics, Vol. 398 (2019), Iss. P.108826

    https://doi.org/10.1016/j.jcp.2019.07.025 [Citations: 11]