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.
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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.
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