Open Access

ARTICLE

Energy-Conserving Local Time Stepping Based on High-Order Finite Elements for Seismic Wave Propagation Across a Fluid-Solid Interface

by Ronan Madec¹, Dimitri Komatitsch¹, Julien Diaz³

1 Université de Pau et des Pays de l’Adour, CNRS and INRIA Magique-3D. Laboratoire de Modélisation et Imagerie en Géosciences UMR 5212, Avenue de l’Université, 64013 Pau cedex, France. E-mail: ronan.madec@gmail.com, dimitri.komatitsch@univ-pau.fr
2 Institut universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France.
3 INRIA Magique-3D, Université de Pau et des Pays de l’Adour and CNRS. Laboratoire de Mathématiques et de leurs Applications UMR 5142, Avenue de l’Université, 64013 Pau cedex, France. E-mail: julien.diaz@inria.fr

Computer Modeling in Engineering & Sciences 2009, 49(2), 163-190. https://doi.org/10.3970/cmes.2009.049.163

Abstract

When studying seismic wave propagation in fluid-solid models based on a numerical technique in the time domain with an explicit time scheme it is often of interest to resort to time substepping because the stability condition in the solid part of the medium can be more stringent than in the fluid. In such a case, one should enforce the conservation of energy along the fluid-solid interface in the time matching algorithm in order to ensure the accuracy and the stability of the time scheme. This is often not done in the available literature and approximate techniques that do not enforce the conservation of energy are used instead. We introduce such an energy-conserving local time stepping method, in which we need to solve a linear system along the fluid-solid interface. We validate it based on numerical experiments performed using high-order finite elements. This scheme can be used in any other numerical method with a diagonal mass matrix.

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