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 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.

  • 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 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0171}, url = {http://global-sci.org/intro/article_detail/cicp/10527.html} }
TY - JOUR T1 - Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects JO - Communications in Computational Physics VL - 1 SP - 264 EP - 295 PY - 2018 DA - 2018/01 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2016-0171 UR - https://global-sci.org/intro/article_detail/cicp/10527.html KW - Acoustic scattering, second-kind boundary integral equations, Galerkin boundary element methods. AB -

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.

Xavier Claeys, Ralf Hiptmair & Elke Spindler. (2020). Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects. Communications in Computational Physics. 23 (1). 264-295. doi:10.4208/cicp.OA-2016-0171
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