AN ELLIPSOIDAL ACOUSTIC INFINITE ELEMENT

In previous papers the authors presented new 3-D time-harmonic prolate and oblate spheroidal acoustic infinite elements, based on new prolat e and oblate spheroidal multipole expansions, for modeling acoustic fi elds in unbounded domains. Here, we present the development of an elli psoidal infinite element, which is the logical generalization of those elements. This development is also based on a new multipole expansion as well as a new system of ellipsoidal coordinates. The element stiff ness, radiation-damping and mass matrices are developed and presented in sufficient detail to enable their software implementation. Both the new coordinate system and the new element include the previous sphero idal coordinate systems and spheroidal elements as limiting cases. The refore, all the previously reported performance data for the spheroida l elements apply to this ellipsoidal element when used in spheroidal f orm. Since the three axes of an ellipsoid can be chosen independently, an ellipsoid can circumscribe any structural shape at least as closel y, and generally more closely, than a prolate or oblate spheroid. The resulting reduction in size of the finite computational domain will re sult in even greater computational speeds than those already reported for the spheroidal elements. The element may be used to model problems in free-space (4 pi steradians), half-space (2 pi), quarter-space (pi ) or eighth-space ( pi/2). Since this infinite element provides maximu m computational efficiency for structures of all shapes, software elem ent libraries would need only this one element for all problems in unb ounded domains. (C) 1998 Elsevier Science S.A. All rights reserved.