A second-kind Galerkin boundary element method for scattering at composite objects (Q2264047)

The paper is devoted to second-kind boundary integral equations for acoustic scattering at bounded composite objects. Using multi-potentials the authors develop a variational formulation in \(L^2\) for a second-kind boundary integral equation with the skeleton Cauchy data as unknowns. Even for nonsmooth domains and junction points the equation hat the form Identity + compact operator. Then under the assumption of unique solvability the convergence of the Galerkin discretization is guaranteed. The authors investigate the Galerkin boundary element discretization from a theoretical and algorithmic point of view. Numerical studies demonstrate the competitive accuracy and superior conditioning of the novel approach compared to the Galerkin method for first-kind boundary integral formulations of acoustic scattering problems.