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Fictitious Domains, Mixed Finite Elements and Perfectly Matched Layers for 2D Elastic Wave Propagation

Eliane Bécache 1 Patrick Joly 1 Chrysoula Tsogka 1
1 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR2706
Abstract : We design a new and efficient numerical method for the modelization of elastic wave propagation in domains with complex topographies. The first specificity is the use of the fictitious domain method to take into account the boundary condition on the topography: the elastodynamic problem is extended in a domain with simple geometry, which permits the use of regular meshes. The free boundary condition is enforced introducing a Lagrange multiplier, defined on the boundary and discretized with a non uniform boundary mesh. This leads us to consider the first order velocity-stress formulation of the equations and particular mixed finite elements. These elements have three main non-standard properties: they take into account the symmetry of the stress tensor, they are compatible with mass lumping techniques and lead to explicit time discretisation schemes, and they can be coupled with the Perfectly Matched Layer technique for the modeling of unbounded domains. Our method permits to model wave propagation in complex media such as anisotropic, heterogeneous media with complex topographi- es or/and with cracks, as it will be illustratred by several numerical experiments.
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Submitted on : Wednesday, May 24, 2006 - 10:50:20 AM
Last modification on : Wednesday, May 11, 2022 - 12:06:04 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:21:26 PM


  • HAL Id : inria-00072764, version 1



Eliane Bécache, Patrick Joly, Chrysoula Tsogka. Fictitious Domains, Mixed Finite Elements and Perfectly Matched Layers for 2D Elastic Wave Propagation. [Research Report] RR-3889, INRIA. 2000. ⟨inria-00072764⟩



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