Volume 23, Issue 1
Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects

Xavier Claeys, Ralf Hiptmair & Elke Spindler

Commun. Comput. Phys., 23 (2018), pp. 264-295.

Published online: 2018-01

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  • 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 secondkind 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 multipotentials, we derive variational second-kind boundary integral equations posed in L 2 (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.

  • Keywords

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

  • AMS Subject Headings

65N12, 65N38, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-264, author = {}, title = {Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {1}, pages = {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 secondkind 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 multipotentials, we derive variational second-kind boundary integral equations posed in L 2 (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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0171}, url = {http://global-sci.org/intro/article_detail/cicp/10527.html} }
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