Efficient Unsplit Perfectly Matched Layers for Finite-Element Time-Domain Modeling of Elastodynamics

Abstract

AbstractThe perfectly matched layer (PML) is a highly efficient absorbing boundary used for the numerical modeling of an elastic wave equation on an unbounded domain. In this work, the authors are concerned with a second-order unsplit PML for transient elastodymanic problems in a semi-plane medium with finite-element approximations. First, based on the concept of stretched coordinates, an efficient unsplit PML formulation is proposed without higher derivatives. Then a finite-element time-domain scheme of a second-order PML in a displacement formulation is developed, in which the Galerkin method is used in space discretization and a Newmark-type scheme is employed for time stepping. Inside the absorbing layer, only one auxiliary vector is required. Hence, the scheme is cheap to implement and easily coupled with standard finite-element methods. Finally, the accuracy and efficiency of the present unsplit PML is demonstrated in numerical examples with a finite-element time-domain scheme.