Multi-trace boundary integral formulation for acoustic scattering by composite structures

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