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

Xavier Claeys 1, 2 Ralf Hiptmair 3 Elke Spindler 3 
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
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. We recast it into a variational problem set in L2 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.
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Submitted on : Tuesday, November 26, 2013 - 11:44:42 PM
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Xavier Claeys, Ralf Hiptmair, Elke Spindler. A Second-Kind Galerkin Boundary Element Method for Scattering at Composite Objects. BIT Numerical Mathematics, 2015, 55 (1), pp.33-57. ⟨10.1007/s10543-014-0496-y⟩. ⟨hal-00909835⟩



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