On constructing the solution to the exterior Dirichlet problem for the Helmholtz equation

AbstractIn this paper a method is given for constructing the solution to the exterior Dirichlet problem for the Helmholtz equation in three dimensions. This method is modeled after the procedure of Colton and Kleinman (Proc. Roy. Soc. Edin. 86A(1980), 29–42) for solving the corresponding two-dimensional problem. The scattering problem is reformulated as an integral equation and it is shown that its solution can be represented as a convergent Neumann series for small values of the wave number. Comparisons are made between the present method and known results. Examples are given which illustrate the method