Application of the BIE Method to Sound Radiation Problems Using an Isoparametric Element

Abstract

This paper discusses the application of the Boundary Integral Equation method for the numerical solution of radiation problems governed by Helmholtz’s equation. In particular, we introduce an isoparametric element formulation in which both the surface geometry and the acoustic variables on the surface of the radiating body are represented by quadratic shape functions within the local coordinate system. A general result for the surface velocity potential is derived. This result includes the case where the surface may have a nonunique normal (e.g., at the edge of a body). The Boundary Integral Equation Method is used to obtain numerical solutions for three radiation problems involving spherical and cubical geometry. The numerical results are compared with exact analytical solutions. The problem of nonuniqueness of the solution at certain frequencies equal to the eigenfrequencies of the corresponding (but physically unrelated) interior problem is illustrated.