A Non-Splitting PML for Elastic Waves in Polar Coordinates and Its Finite Element Implementation

Abstract

In the solving of the elastic wave equations with the numerical approximation techniques, the absorbing boundary conditions had been widely used to truncate the infinite-space simulation to a finite-space one. The perfect matched layer (PML) technique as an absorbing boundary condition had exhibited excellent absorbing efficiency in the forward simulation of the elastic wave equation formulated in rectangular coordinates. Based on the stretched coordinate concept, an advanced non-splitting-field perfect matched layer (non-splitting PML) equation for elastic waves was formulated in the polar coordinate system. Through the introduction of integrated complex variables in the radial direction into the auxiliary functions, the PML formulation was extended in polar coordinates in view of the 2nd-order elastic wave equation with displacements as basic unknowns. In addition, aimed at the time-domain cases and with the finite-element method for space discretization, the finite-element time-domain (FETD) scheme in standard displacement-based formulation was presented. The scheme for the special cases in axisymmetric polar coordinates was also given. The effectiveness and validity of the present non-splitting PML formulation are demonstrated with several numerical examples.