Boundary integral formulation of the first kind for acoustic scattering by composite structures

Abstract

We study the scattering of an acoustic wave by an object composed of several adjacent sub-domains with different material properties. For this problem we derive an integral formulation of the first kind. This formulation involves two Dirichlet data and two Neumann data at each point of each interface of the diffracting object. This formulation is immune to spurious resonances, and it satisfies a stability property that ensures quasi-optimal convergence of conforming Galerkin boundary element methods. Besides, the operator of this formulation satisfies a relation similar to the standard Calderon identity.