Second-Kind Boundary Integral Equations for Scattering at Composite Partly Impenetrable Objects (Communications in Computational Physics, 2018)
We consider acoustic scattering of time-harmonic waves at objects composedof several homogeneous parts. Some of those may be impenetrable, giving riseto Dirichlet boundary conditions on their surfaces. We start from the recent second-kindboundary integral approach of [X. Claeys, and R. Hiptmair, and E. Spindler. Asecond-kind Galerkin boundary element method for scattering at composite objects. BIT NumericalMathematics, 55(1):33-57, 2015] for pure transmission problems and extendit to settings with essential boundary conditions. Based on so-called global multi-potentials,we derive variational second-kind boundary integral equations posed inL2(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 numbersof Galerkin matrices obtained with discontinuous piecewise polynomial boundaryelement spaces. They also confirm competitive accuracy of the numerical solutionin comparison with the widely used first-kind single-trace approach.