The numerical solution of the exterior dirichlet problem for Helmholtzʹs equation via modified greenʹs functions approach

In the 1970s, a modified Greenʹs function approach for solving the Helmholtz equation was proposed by Jones and Ursell, and in the 1980s was clarified by Kleinman, Roach and Kress. But to date, there are no numerical results available for this approach. In this paper, a global Galerkin method is used to numerically solve the exterior Dirichlet problem for the Helmholtz equation in three dimensions based on Jonesʹ modified integral equation approach. Theoretical and computational details of the method are presented.