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Journal Articles Communications in Computational Physics Year : 2012

Performance Analysis of a High-Order Discontinuous Galerkin Method. Application to the Reverse Time Migration

Abstract

This work pertains to numerical aspects of a finite element method based discontinuous functions. Our study focuses on the Interior Penalty Discontinuous Galerkin method (IPDGM) because of its high-level of flexibility for solving the full wave equation in heterogeneous media. We assess the performance of IPDGM through a comparison study with a spectral element method (SEM). We show that IPDGM is as accurate as SEM. In addition, we illustrate the efficiency of IPDGM when employed in a seismic imaging process by considering two-dimensional problems involving the Reverse Time Migration.
High-order Discontinuous Galerkin Methods (DGM) are now routinely used for simulation of wave propagation, especially for geophysical applications. However, to fully take full advantage of the high-order space discretization, it is relevant to use a high-order time discretization. Hence, DGM are currently coupled with ADER schemes, which leads to high-order explicit time schemes, but requires the introduction of auxiliary unknowns. The memory can thus be considerably cluttered up. In this work, we propose a new high order time scheme, the so-called Nabla-p scheme. This scheme does not increase the storage costs since it is a single step method which does not require introducing auxiliary unknowns. Numerical results show that for a given accuracy, the new scheme requires less computational burden regarding both the memory and the computational costs than the DG-ADER scheme. Résumé. Les méthodes de Galerkin Discontinues (DGM) d'ordré elevé sont maintenant couram-ment utilisées pour la simulation de la propagation des ondes, en particulier pour les applications géophysiques. Cependant, pour profiter pleinement d'une discrétisation en espace d'ordré elevé, il est pertinent d'utiliser une discrétisation en temps d'ordré elevé. C'est pourquoi les DGM sont sou-vent associéesassociéesà des schémas ADER, ce qui conduitàconduità des formulations en temps explicites et d'ordréordré elevé. Toutefois, les méthodes DG-ADER nécessitent d'introduire des inconnue auxiliaire, ce qui peut encombrer considérablement la mémoire. Dans ce travail, nous proposons un nouveau schéma tem-porel d'ordré elevé, le schéma Nabla-p. Ce schéma n'augmente pas les coûts de stockage car il s'agit d'une méthodè a un pas, sans utilisation d'inconnues auxiliaires. Les résultats numériques montrent qu'il nécessite moins d'espace mémoire et qu'il coûte moins cher que la méthode DG-ADER pour une précision donnée.
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Dates and versions

hal-00643334 , version 1 (19-02-2018)

Identifiers

Cite

Caroline Baldassari, Hélène Barucq, Henri Calandra, Bertrand Denel, Julien Diaz. Performance Analysis of a High-Order Discontinuous Galerkin Method. Application to the Reverse Time Migration. Communications in Computational Physics, 2012, 11 (2), pp.660-673. ⟨10.4208/cicp.291209.171210s⟩. ⟨hal-00643334⟩
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