@Article{CiCP-23-264, author = {Xavier Claeys, Ralf Hiptmair and Elke Spindler}, 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.