Numerical difficulties with boundary element solutions of interior acoustic problems

Abstract

Although boundary element methods have been applied to interior problems for many years, the numerical difficulties that can occur have not been thoroughly explored. Various authors have reported artificial damping due to acoustic radiation and low‐frequency breakdowns. In this presentation, it is shown through a simple example problem that the numerical difficulties depend on the solution formulation. When the boundary conditions are imposed directly, the solution suffers from artificial damping due to sound radiation to the farfield. This difficulty can be alleviated by first computing an impedance matrix or admittance matrix, and then using its reactive component to derive the solution for the acoustic field. Numerical computations are used to demonstrate that this technique eliminates artificial damping, but does not correct errors in the reactive components of the impedance or admittance matrices, which then cause nonexistence/nonuniqueness difficulties at the interior resonance frequencies for hard‐wall or pressure release boundary conditions, respectively. It is shown that the admittance formulation is better suited to boundary element computations for interior problems because the resonance frequencies for pressure release boundary conditions do not begin until the smallest dimension of the boundary surface is at least one half of the acoustic wavelength.