Fictitious domains, mixed finite elements and perfectly matched layers for2-D elastic wave propagation

We design a new and efficient numerical method for the modelization of elas tic wave propagation in domains with complex topographies. The main charact eristic is the use of the fictitious domain method for taking into account the boundary condition on the topography: the elastodynamic problem is exte nded in a domain with simple geometry, which permits us to use a regular me sh. The free boundary condition is enforced introducing a Lagrange multipli er, defined on the boundary and discretized with a nonuniform boundary mesh . This leads us to consider the first-order velocity-stress formulation of the equations and particular mixed finite elements. These elements have thr ee main nonstandard properties: they take into account the symmetry of the stress tensor, they are compatible with mass lumping techniques and lead to explicit time discretization schemes, and they can be coupled with the Per fectly Matched Layer technique for the modeling of unbounded domains. Our m ethod permits us to model wave propagation in complex media such as anisotr opic, heterogeneous media with complex topographies, as it will be illustra ted by several numerical experiments.