A meshfree method with plane waves for elastic wave propagation problems

In this paper, we address the meshfree numerical solution of time-harmonic linear elastic wave propagation problems in homogeneous media. In particular, we analyze the asymptotic behavior of the method of fundamental solutions (MFS) with source points located far away from the domain of interest. The asymptotic MFS is shown to be equivalent to a Trefftz method, here referred to as the plane waves method (PWM), based on superposition of shear and compressional elastic plane waves with different directions of propagation. Several numerical examples are included in order to illustrate the equivalence between the asymptotic MFS and the PWM. The convergence and stability of the PWM are also analyzed in smooth settings.