Numerical studies of conjugated infinite elements for acoustical radiation

Aspects of conjugated infinite element schemes for unbounded wave problems are reviewed and a general formulation is presented for elements of variable order based on separable shape functions expressed in terms of prolate and oblate spheroidal coordinates. The formulation encompasses both "conjugated Burnett" and "Astley-Leis" elements. The performance of the two approaches is compared for steady multipole wave fields and the effect of the radial basis on the condition number of the resulting equations is discussed. Transient formulations based on these elements are derived and methods for solving the resulting transient equations are discussed. The use of an implicit time stepping scheme coupled with an indirect iterative solver is shown to give fast transient solutions which do not require matrix inversion.