Numerical treatment of acoustic problems with the hybrid boundary element method

The symmetric hybrid boundary element method in the frequency and time doma in is introduced for the computation of acoustic radiation and scattering i n closed and infinite domains. The hybrid stress boundary element method in a frequency domain formulation is based on the dynamical Hellinger-Reissne r potential and leads to a Hermitian, frequency-dependent stiffness equatio n. As compared to previous results published by the authors, new considerat ions concerning the interpretation of singular contributions in the stiffne ss matrix are communicated. On the other hand, the hybrid displacement boun dary element method for time domain starts out from Hamilton's principle fo rmulated with the velocity potential. The field variables in both formulati ons are separated into boundary variables, which are approximated by piecew ise polynomial functions, and domain variables, which are approximated by a superposition of singular fundamental solutions, generated by Dirac distri butions, and generalized loads, that are time dependent in the transient ca se. The domain is modified such that small spheres centered at the nodes ar e subtracted. Then the property of the Dirac distribution, now acting outsi de the domain, cancels the remaining domain integral in the hybrid principl e and leads to a boundary integral formulation, incorporating singular inte grals. In the time domain formulation, an analytical transformation is empl oyed to transform the remaining domain integral into a boundary one. This a pproach results in a linear system of equations with a symmetric stiffness and mass matrix. Earlier 2D results are generalized in the present paper by a 3D implementation. Numerical results of transient pressure wave propagat ion in a closed domain are presented. (C) 2001 Elsevier Science Ltd. All ri ghts reserved.