The impedance problem for the propagative helmholtz equation in interior multiply connected domain

The impedance problem for the propagative Helmholtz equation in the interior multiply connected domain is studied in two and three dimensions by a special modification of a boundary integral equation method. Additional boundaries are introduced inside interior parts of the boundary of the domain. 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.