A gradient formulation of the Helmholtz integral equation for acoustic radiation and scattering

Abstract

A method of overcoming the problem of nonuniqueness in the discretized Helmholtz integral equation is described, based on a partial application of the Helmholtz gradient formulation of Burton and Miller [Proc. R. Soc. London, Ser. A 323, 201–210 (1971)]. The numerical implementation is designed to be compatible with a finite-element structural analysis, and uses boundary elements of the quadratic isoparametric type. The method is illustrated for scattering from a sphere, and for radiation by a piston vibrating in the end of a cylinder, with consistent results being obtained across a wide frequency range. The additional computation is of the order of 35% of that required for the standard formulation.