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It is well known that the elastic wave propagation predicted by the FEM suffers from the difficulty to correctly reproduce the unbounded media: spurious waves are reflected at the FEM model at the artificial boundaries. Variant techniques may be introduced to reduce the spurious reflections at the boundaries, such as the infinite elements, the absorbing boundary conditions or the perfect matched layers. Nonetheless, the most efficient strategy, such as the perfect matched layer, leads to an important implementation effort in existing FE softwares. Recently, a simplified approach proposed by Semblat et al. (2010) consists in introducing classical Rayleigh formulation in a layer subdomain, surrounding the domain under investigation; the purpose of this artificial layer is to damp the incident seismic waves while minimizing the spurious reflected waves towards the studied domain. The objective of this work is to enhance this methodology by taking advantage of the subdomain methods. The GC method, proposed ten years ago by Combescure and Gravouil, enables to decompose a finite element mesh into several partitions and to use in each partition the suitable time integrator with its own time step. Therefore, the coupling method is heterogeneous, allowing to couple different time integrators and multi-time steps in the sense that very different time steps depending on the subdomains can be adopted. An external coupling software, based on the GC method, are developed to enable multi-time step explicit/implicit co-computations. It makes to interact in time an explicit FE code (Europlexus), associated with fine time step for the domain of interest, with an implicit FE code (Cast3m) handling the absorbing boundary layers by using a Rayleigh viscous damping matrix. Large time steps can be adopted for the absorbing boundary layers. The reduction of the spurious wave reflections at the interface has been optimized as well as the ability of the absorbing layers to damp the transmitted waves. The relevance and the numerical efficiency of the multi-time step implicit absorbing boundary layer strategy are compared with classical absorbing boundary conditions.

A MULTI-DIRECTIONAL ABSORBING LAYER FOR SEISMIC WAVE PROPAGATION IN UNBOUNDED DOMAIN BY USING HETEROGENEOUS MULTI-TIME STEP SUBDOMAIN METHODS.