A 3-DIMENSIONAL ACOUSTIC INFINITE ELEMENT BASED ON A PROLATE SPHEROIDAL MULTIPOLE EXPANSION

This paper describes a new three-dimensional (3-D) time-harmonic acoustic infinite element for modeling acoustic fields in exterior domains, typically surrounding a structure. This ''prolate spheroidal infinite element'' is based on a new multipole expansion that is the exact solution for arbitrary scattered and/or radiated fields exterior to a prolate spheroid of any eccentricity. A combination of both prolate and oblate spheroidal infinite elements (the latter to be published separately) provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This new prolate element has symmetric matrices that are as cheap to generate as for 2-D elements because only 2-D integrals need to be numerically evaluated. The prolate element (along with a symmetric-matrix fluid-structure coupling element, also to be published separately) fits naturally into purely structural finite element codes, thereby providing a structural acoustics capability. For the class of coupled structural acoustic problems studied so far, this approach is two to three orders of magnitude faster, for the same accuracy, than the boundary element method (BEM), which is based on the surface Helmholtz integral equation. Experience with developing and using both BEM and infinite-element codes has revealed that the severe computational inefficiency of the BEM limits practical 3-D structural acoustic problems to low frequencies and simple structures, whereas this new infinite-element approach can handle the full range of frequencies and structural complexities that are encountered in purely structural analyses, at little additional cost.