SMART layers: A simple and robust alternative to PML approaches for elastodynamics

Abstract

For considering elastic seismic wave propagation in large domains, efficient absorbing boundary conditions are required with numerical modelling in finite domains. Since their introduction by Bérenger, the perfectly matched layers (PML) has become the state-of-the art method because of its efficiency and ease of implementation. However, for anisotropic media, theoretical analysis and numerical experiments show that the PML method is amplifying, that is it exhibits numerical instabilities. Numerical experiments can also exhibit numerical instabilities of the PML when dealing with long time simulations even for isotropic media, especially for finite element methods in unstructured grids. Recently, a new method, called SMART layers approach, has been proposed. This method is shown to be stable even for anisotropic media. The drawback is that the SMART layers are not perfectly matched. We have implemented this new approach in a discontinuous Galerkin method and we illustrate that this method does not exhibit numerical instabilities while PML do for an isotropic elastodynamic simulation. We show that this approach is also competitive with respect to the PML method in terms of efficiency and computational cost.