Astley, R.J. (2000) Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. International Journal for Numerical Methods in Engineering, 49 (7), 951-976. (doi:10.1002/1097-0207(20001110)49:7<951::AID-NME989>3.0.CO;2-T).
Abstract
Infinite element schemes for unbounded wave problems are reviewed and a procedure is presented for assessing their performance. A general computational scheme is implemented in which orthogonal functions are used for the transverse interpolation within the infinite element region. This is used as a basis for numerical studies of the effectiveness of various combinations of the radial test and trial functions which give rise to different conjugated and unconjugated formulations. Results are presented for the test case of a spherical radiator to which infinite elements are directly attached. Accuracy of the various schemes is assessed for pure multipole solutions of arbitrary order. Previous studies which have indicated that the conjugated and unconjugated schemes are more effective in the far and near fields, respectively, are confirmed by the current results. All of the schemes tested converge to the exact solution as radial order increases. All are however susceptible to ill conditioning. This places practical restrictions on their effectiveness at high radial orders. A close relationship is demonstrated between the discrete equations which arise from first-order infinite element schemes and those derived from the application of more traditional, local non-reflecting boundary conditions.
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