P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problems

The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd.

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