A fast volume integral equation method for elastic wave propagation in a half space

A fast method for solving the volume integral equation is developed for scattering analysis of elastic wave propagation in a half space. The proposed method applies the fast generalized Fourier transform and inverse transform formulated in the present study to the Krylov subspace method. The amount of calculations required for the proposed method is O(NlogN), where N is the number of grid points used to model the elastic half space. Furthermore, the MPI parallel algorithm for the generalized Fourier transform is presented for further reduction of the CPU time. Numerical calculations are performed in order to examine the effects of the number of sampling grid points as well as their intervals on the solutions of the volume integral equation and the CPU time required for the analysis. In addition, comparisons of the proposed method with the previous method based on the trapezoidal approach ( Touhei, 2009) are also performed in order to discuss the properties of the solution of the present method.