Hybrid boundary element formulation for acoustic wave propagation

Abstract

The so-called hybrid stress boundary element method (HSBEM) is introduced in a frequency domain formulation for the computation of acoustic radiation and scattering in closed and in finite domains. Different from other boundary element formulations, the HSBEM is based on an extended Hellinger-Reissner variational principle and leads to a Hermitian, frequency-dependent stiffness equation. Due to this, the method is very well suited for treating fluid structure interaction problems since the effort for the coupling the structure, discretized by a finite elements, and the fluid, discretized by the HSBEM is strongly reduced. To arrive at a boundary integral formulation, the field variables are separated into boundary variables, which are approximated by piecewise polynomial functions, and domain variables, which are approximated by a superposition of singular fundamental solutions weighed by source strength. This approximation cancels the domain integral over the equation of motion in the hybrid principle and leads to a boundary integral formulation, incorporating singular integrals. Comparing to previous results published by the authors, new considerations concerning the interpretation of singular contributions in the stiffness matrix for exterior domain problems are communicated here.