Method of interior boundaries for the impedance problem in scattering theory

摘要

The impedance problem for the Helmholtz equation in the exterior of several bodies (obstacles) is studied in two and three dimensions by a special modification of the boundary integral equation method. This modification can be called `Method of interior boundaries', because additional boundaries are introduced inside scattering bodies. The solution of the problem is obtained in the form of a single layer potential on the whole boundary. The density in the potential satisfies the uniquely solvable Fredholm equation of the second kind and can be computed by standard codes. In fact our method holds for any positive wave numbers. The Neumann problem is a particular case of our problem.