A mesh-free finite-difference method for elastic wave propagation in the frequency-domain

We developed an innovative finite-difference method for elastic wave propagation in the frequency-domain. The method is a class of mesh-free method which can discretize governing equations without a restriction of regular lattice grid structure. We investigated the performance of the proposed method using the dispersion analyses and numerical experiments. The dispersion analyses for regular and irregular grid distributions show that quasi-uniform grid distribution can reduce the dispersion error. For a regular grid distribution, the proposed method has the accuracy equivalent to the average-derivative finite-difference method under the same resolution. Numerical experiments demonstrate that the adaptive grid distribution can be used to simulate elastic wave propagation. Since an irregular grid distribution is not used in conjunction with a mesh generation process, this feature can reduce time for initial pre-processing mesh construction. We also investigate the computational cost by comparing the calculation time of the proposed method with that of the average-derivative finite-difference method. The comparison indicates that the proposed method can provide efficient calculation results by using adaptive resolution to the velocity structure.