An effective numeric method for different formulations of the elastic wave propagation problem in isotropic medium.

Abstract

This paper shows how the Generalized Finite Difference Method allows the same schemes in differences to be used for different formulations of the wave propagation problem. These formulations present pros and cons, depending on the type of boundary and initial conditions at our disposal and also the variables we want to compute, while keeping additional calculations to a minimum. We obtain the explicit schemes of this meshless method for different possible formulations in finite differences of the problem. Criteria for stability and convergence of the schemes are given for each case. The study of the dispersion of the phase and group velocities presented in previuos paper of the authors is also completed here. We show the application of the propounded schemes to the wave propagation problem and the comparison of the efficiency, convenience and accuracy of the different formulations.