A direct boundary integral equation method for the acoustic scattering problem

Abstract

This paper presents a direct boundary integral equation method for solving the exterior Neumann problem of the Helmholtz equation which is a mathematical formulation of the acoustic scattering problem at a perfectly hard body. It is proved that the integral equation obtained from the Helmholtz representation is equivalent to the original boundary value problem and it has a unique solution in a suitable Sobolev space in the framework of pseuo-differential operators. Moreover, the numerical treatment and error estimate are given by using a Galerkin approximation.