Numerical evaluation of 3D time-harmonic elastodynamic Green?s function and its derivatives for anisotropic solids

The paper presents a fast and accurate numerical technique for evaluation of the 3D time-harmonic elastody-namic Green's function and its derivatives for anisotropic solids. Following Wang & Achenbach the Green's function is presented in the form of the sum of singular (static) and regular parts, which are both reduced to integrals over a unit sphere. Singular part and its derivatives are then reduced to the integrals over a unit circle, which can be efficiently (fast and accurately) evaluated using the trapezoid rule, which is exponentially convergent for integrals over the period of a periodic integrand. The regular time-harmonic parts are presented through the double integrals. The outer integral is also efficiently evaluated using the trapezoid rule. A special quadrature is developed for evaluation of the inner integral, which accounts for the highly-oscillating behavior of the integrand. Numerical examples are presented, which shows the advantage of the proposed technique over others.