The skeleton equation method for acoustic transmission problems with varying coefficients

Abstract

In this paper we describe the skeleton equation method, to transform a three‐dimensional acoustic transmission problem with variable coefficients and mixed boundary conditions to a non‐local equation on a two‐dimensional skeleton, without relying on an explicit knowledge of Green's function. This is achieved introducing and analyzing abstract layer potentials as solutions of auxiliary coercive full space transmission problems; they satisfy jump conditions across domain interfaces. The novelty in this paper is that we reduce acoustic scattering problems with possible variable coefficients to boundary integral equation on the domain skeleton, and we prove frequency exlicit continuity and coercivity estimates. The resulting equations are stated in a form such that standard boundary element methods can be applied for the discretization.