A new approach to reduction of the Neumann problem in acoustic scattering to a non-hypersingular integral equation

摘要

The Neumann problem for the propagative 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 the '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. [References: 24]