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A Second-Kind Galerkin Boundary Element Method for Scattering at Composite Objects

by X. Claeys and R. Hiptmair and E. Spindler

(Report number 2013-13)

Abstract
We consider the scattering of time-harmonic acoustic waves at objects composed of several homogeneous parts with different material properties. In \([\)X. Claeys, A single trace integral formulation of the second kind for acoustic scattering, Report 2011-14, SAM, ETH Zürich\(]\) a novel second-kind boundary integral formulation for this scattering problem was proposed that relies on skeleton Cauchy data as unknowns. We recast it into a variational problem set in \(L^{2}\) and investigate its Galerkin boundary element discretization from a theoretical and algorithmic point of view. Empiric studies demonstrate the competitive accuracy and superior conditioning of the new approach compared to a widely used Galerkin boundary element approach based on a first-kind boundary integral formulation.

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

@Techreport{CHS13_509,
  author = {X. Claeys and R. Hiptmair and E. Spindler},
  title = {A Second-Kind Galerkin Boundary Element Method for Scattering at Composite Objects},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-13},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-13.pdf },
  year = {2013}
}

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