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

Abstract

This report is concerned with the problem of obtaining a unique solution for radiation 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. The use of CHIEF is illustrated with numerical radiation experiments for the sphere and the finite cylinder. CHIEF is compared to the Helmholtz gradient formulation (HGF) for circumventing nonuniqueness and is found to yield a more accurate solution, in at least one published example. 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. [Work supported in part by ONR.]