A Second-Kind Galerkin Boundary Element Method for Scattering at Composite Objects
Résumé
We consider the scattering of time-harmonic acoustic waves at objects composed of several homogeneous parts with different material properties. In [X. Claeys, A single trace integral formulation of the second kind for acoustic scattering, Report 2011-14, SAM, ETH Zürich] a novel second-kind boundary integral formulation for this scattering problem was proposed. We recast it into a variational problem set in L2 and investigate its Galerkin boundary element discretization from a theoretical and algorithmic point of view. Empiric studies demonstrate the competitive accuracy and superior conditioning of the new approach compared to a widely used Galerkin boundary element approach based on a first-kind boundary integral formulation.