Residue approach for evaluating the 3D anisotropic elastic Green’s function: multiple roots

A numerical algorithm based upon the residue calculus for computing the three-dimensional anisotropic elastic Green’s function and its derivatives has been presented by, among the others, Sales and Gray. Although this residue approach is in general faster than the standard Wilson–Cruse interpolation scheme, the convergence rate and accuracy can seriously degrade in the neighborhood of a non-simple pole. In this paper, explicit expressions, also based on the residue calculus, are obtained for computing the Green’s function and its first-order derivatives in the presence of a multiple root. Further, the computation time for the residue algorithm proposed here has been significantly reduced by implementing the double-subscript-notation for the elastic constants that define the Christoffel tensor. q 2005 Elsevier Ltd. All rights reserved.