The Dirichlet problem for the propagative Helmholtz equation in a 2-D exterior domain bounded by closed curves and open arcs

The Dirichlet problem for the 2-D Helmholtz equation in an exterior domain bounded by closed curves and open arcs is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind and index zero, which is uniquely solvable. It means, that the solution can be computed by standard codes.