Perfectly matched layers for transient elastodynamics of unbounded domains

One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non-tangential angles-ofincidence and of all non-zero frequencies. In a recent work [Computer Methods in Applied Mechanics and Engineering 2003; 192:1337–1375], the authors presented, inter alia, time-harmonic governing equations of PMLs for anti-plane and for plane-strain motion of (visco-)elastic media. This paper presents (a) corresponding time-domain, displacement-based governing equations of these PMLs and (b) displacement-based finite element implementations of these equations, suitable for direct transient analysis. The finite element implementation of the anti-plane PML is found to be symmetric, whereas that of the plane-strain PML is not. Numerical results are presented for the anti-plane motion of a semi-infinite layer on a rigid base, and for the classical soil–structure interaction problems of a rigid strip-footing on (i) a half-plane, (ii) a layer on a half-plane, and (iii) a layer on a rigid base. These results demonstrate the high accuracy achievable by PML models even with small bounded domains