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

The Neumann problem for the propagative Helmholtz equation inthe exterior of several bodies (obstacles) is studied in twoand three dimensions by a special modification of the boundaryintegral equation method. This modification can be called the'method of interior boundaries', because additional boundariesare introduced inside scattering bodies. The solution of theproblem is obtained in the form of a single layer potentialon the whole boundary. The density in the potential satisfiesthe uniquely solvable Fredholm equation of the second kind andcan be computed by standard codes. In fact our method holdsfor any positive wave numbers.