École Nationale Supérieure de
Techniques Avancées

Abstract

We consider the propagation of elastic waves in unbounded domains. A new formulation of the linear elasticity system as an H (div)−L2 system enables us to use the “mixed spectral finite element method”, This new method is based on the definition of new spaces of approximation and the use of mass-lumping. It leads to an explicit scheme with reduced storage and provides the same solution as the spectral finite element method. Then, we modelize unbounded domains by using Perfectly Matched Layers. Instabilities in the PML in the case of particular 2D elastic media are pointed out and investigated. The numerical method is validated and tested in the case of acoustic and elastic realistic models. A plane wave analysis gives results about numerical dispersion and shows that meshes adapted to the physical and geometrical properties of the media are more accurate than the others. Then, an extension of the method to fluid-solid coupling is introduced for 2D seismic propagation.