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.