A second-kind Galerkin boundary element method for scattering at composite objects

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• 作者：Xavier Claeys (1) (2) (3)
  Ralf Hiptmair (4)
  Elke Spindler (4)
  
  1. Laboratoire Jacques-Louis Lions ; Sorbonne Universit茅s ; UPMC Univ Paris 06 ; UMR 7598 ; 75005聽 ; Paris ; France
  2. Laboratoire Jacques-Louis Lions ; CNRS ; UMR 7598 ; 75005聽 ; Paris ; France
  3. INRIA-Paris-Rocquencourt ; EPC Alpines ; Domaine de Voluceau ; BP105 ; 78153聽 ; Le Chesnay Cedex ; France
  4. Swiss Federal Institute of Technology ; Zurich ; Switzerland
  
• 关键词：Acoustic scattering ; Second ; kind boundary integral equations ; Galerkin boundary element methods ; 65N12 ; 65N38 ; 65R20
• 刊名：BIT Numerical Mathematics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：55
• 期：1
• 页码：33-57
• 全文大小：835 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Numeric Computing
  Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9125

文摘

We consider the scattering of time-harmonic acoustic waves at objects composed of several homogeneous parts with different material properties. In Claeys (A single trace integral formulation of the second kind for acoustic scattering, 2011), 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.