Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable 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, Institut National des Sciences Mathématiques et de leurs Interactions
3 Seminar of Applied Mathematics
SAM - Seminar of Applied Mathematics [Zürich]
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 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] and extend it to this setting. Based on so-called global multi-potentials, we derive variational second-kind boundary integral equations posed in $L^2(\Sigma)$, where $\Sigma$ 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.
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Pré-publication, Document de travail
2015
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Xavier Claeys, Ralf Hiptmair, Elke Spindler. Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects. 2015. 〈hal-01251240〉

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