The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations

This article is concerned with the problem of obtaining a unique solution for radiation and scattering problems at characteristic wavenumbers when a boundary integral equation formulation is used. It is shown that the combined Helmholtz integral equation formulation (CHIEF) method works even when numerous interior points lie exactly on nodal surfaces of a mode corresponding to an eigenfrequency of the related interior problem, when at least one interior point does not lie on a nodal surface. CHIEF is compared to the Helmholtz gradient formulation (HGF) for circumventing nonuniqueness and is found to yield a more accurate solution. A procedure is used to indicate the solution error when using integral equation methods, with or without a technique to circumvent nonuniqueness. This procedure uses the velocity potential of an interior point as an indicator of solution error. In all cases considered, the interior potential correctly indicated a good or bad solution; whereas the matrix condition number falsely indicated a bad solution in several instances.