Prolate and oblate spheroidal acoustic infinite elements Original Research Article

In a previous paper, the first author presented a new 3-D time-harmonic prolate spheroidal acoustic infinite element for modeling acoustic fields in exterior domains. Here, we present the development of the logical companion to that element, viz. an oblate spheroidal infinite element. Both elements are based on multipole expansions for the acoustic field in spheroidal coordinates developed by the second author in a separate paper, recently submitted for publication. For completeness, an outline of the proofs of convergence of these expansions is included here. Also, essential equations for the previously published prolate spheroidal infinite element are reproduced here in order that this paper can stand as an independent explication of the spheroidal family of infinite elements. It is shown that a choice of prolate or oblate spheroidal infinite elements provides a capability for very efficiently modeling acoustic fields surrounding structures with a wide variety of practical shapes.