TY - JOUR
T1 - Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects
AU - Xavier Claeys, Ralf Hiptmair & Elke Spindler
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 - <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>