GENESIS AND ELIMINATION OF FICTITIOUS RESONANCES IN INTEGRAL METHODS FOR THE EXTERIOR HELMHOLTZ PROBLEM

Abstract

This work is devoted to the study of the spurious frequency spectrum resulting from numerical implementations of the boundary element method for the exterior Helmholtz problem with Neumann boundary conditions. A perturbation occurs, not because the original problem fails to have a unique solution, but due to the representation used for the field.

Together with a recently developed fully desingularized boundary element method that implies superior numerical accuracy, it is demonstrated that the CHIEF method can be highly improved by taking first-order and second-order derivatives with suitable constraints on the CHIEF point placement and extended to intermediate frequencies. Then, it is shown that using a modified Green’s function based on an interior point or surface, in comparison with the ordinary 3D free space Green’s function, can remove these spurious frequencies. The concepts are illustrated with examples of a scattering wave on a rigid sphere.