Acoustic Green's functions using the Sinc-Galerkin method

Green's functions represent the scattering behaviour of a particular geometry and are required to propagate acoustic disturbances through complex geometries using integral methods. The versatility of existing integral methods of acoustic propagation may be greatly increased by using numerical Green's functions computed for more general geometries. We investigate the use of the Sinc-Galerkin method to compute Green's functions for the Helmholtz equation subject to homogeneous Dirichlet boundary conditions. We compare the results to a typical boundary element method implementation. The Sinc-Galerkin procedure demonstrates improved performance on a number of configurations tested in comparison to the BEM. In particular, accuracy comparable to BEM can be achieved in far less time while being less sensitive to both frequency and source position, although the BEM captures the tip of the singularity more completely. The characteristic exponential convergence, as expected, is slower than many Sinc-Galerkin applications due to the presence of the domain singularity typical of Green's functions.