| Popis: |
In many acoustic problems, the radiated sound field is dominated by scattering effects. 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. To this end, we investigate the use of the Sinc-Galerkin method to compute the Green's function 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 Sinc-Galerkin is seen to remain robust despite close proximity of the source point to the boundaries and a coarse, non-uniform distribution of mesh nodes. However, the characteristic exponential convergence is slower than many other Sinc-Galerkin applications (or lost entirely) due to the presence of the domain singularity typical of Green's functions. In addition, we present one possible formulation for homogeneous Neumann boundary conditions (rigid boundaries). |
