@Article{CiCP-23-1,
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 = {<p style="text-align: justify;">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.<em> A
second-kind Galerkin boundary element method for scattering at composite objects.</em> 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
L<sup>2</sup>(Σ), where Σ denotes the union of material interfaces. To suppress spurious resonances,
we introduce a combined-field version (CFIE) of our new method.<br/>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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0171},
url = {https://global-sci.com/article/80010/second-kind-boundary-integral-equations-for-scattering-at-composite-partly-impenetrable-objects}
}