SMART Layers: A Simple and Robust Alternative to PML Approaches for Elastodynamics

Abstract:

Absorbing boundary conditions are required for elastodynamic simulations in finite domains. The Perfectly Matched Layers (PML) have become the state-of-the-art method since its introduction (Berenger 1994). PML approaches have been proved to be very efficient and easy to implement. However, sometimes numerical instabilities originated in the PML layers can appear, even for isotropic media. For anisotropic media, it has been proven that PML have an amplifying behaviour, i.e. numerical instabilities (Becache et al. 2003). For delaying the appearance of these PML instabilities, different pragmatic approaches has been proposed (Meza-Fajarado & Papageorgiou 2008; Martin et al. 2008; Etienne et al. 2010). Yet, there are no guarantee for long-term stabilities and one can observe less efficient absorptions for these adhoc approaches. Recently, a new method, called SMART-layer method, has been proposed and has been shown theoretically to be stable even for anisotropic media (Halpern et al. 2011; Metivier et al. 2013). The SMART-layer method is a robust and simple to design method. However boundary conditions are not perfectly matched even for the continuous case for the SMART-layer method while it is for the PML method. Therefore, stronger reflections are observed at the interface between the domain of interest and the absorbing layers.. We implement this absorbing boundary conditions for the elastodynamics equations in a discontinuous Galerkin scheme and we will show that this numerical implementation does not exhibit numerical instabilities when using different mesh designs while the PML method does for the same simulation of wave propagation in isotropic medium. We finally show how SMART-layer method is competitive with respect to the PML method in terms of efficiency and computational cost, opening roads for systematic implementation of such absorbing boundary conditions in available seismic wave propagation tools.