An ellipsoidal acoustic infinite element

Abstract

In previous papers the authors presented new 3-D time-harmonic prolate and oblate spheroidal acoustic infinite elements, based on new prolate and oblate spheroidal multipole expansions, for modeling acoustic fields in unbounded domains. Here, we present the development of an ellipsoidal 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 stiffness, 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 spheroidal coordinate systems and spheroidal elements as limiting cases. Therefore, all the previously reported performance data for the spheroidal elements apply to this ellipsoidal element when used in spheroidal form. Since the three axes of an ellipsoid can be chosen independently, an ellipsoid can circumscribe any structural shape at least as closely, and generally more closely, than a prolate or oblate spheroid. The resulting reduction in size of the finite computational domain will result in even greater computational speeds than those already reported for the spheroidal elements. The element may be used to model problems in free-space (4π steradians), half-space (2π), quarter-space (π) or eighth-space ( π 2 ). Since this infinite element provides maximum computational efficiency for structures of all shapes, software element libraries would need only this one element for all problems in unbounded domains.