An hp-adaptive discontinuous Galerkin finite-element method for 3-D elastic wave modelling

V. Etienne; E. Chaljub; J. Virieux; N. Glinsky

insu-00565022, version 1

An hp-adaptive discontinuous Galerkin finite-element method for 3-D elastic wave modelling

V. Etienne ¹, E. Chaljub ², J. Virieux ², N. Glinsky ^3, 4

Geophysical Journal International 183 (2010) 941-962

1 : Géoazur (GEOAZUR)
http://geoazur.oca.eu
Université Nice Sophia Antipolis [UNS] – CNRS : UMR6526 – Institut de recherche pour le développement [IRD] – Observatoire de la Côte d'Azur – INSU – Université Pierre et Marie Curie [UPMC] - Paris VI France
2 : Laboratoire de géophysique interne et tectonophysique (LGIT)
http://www-lgit.obs.ujf-grenoble.fr/
CNRS : UMR5559 – Institut de recherche pour le développement [IRD] – LCPC – OSUG – INSU – Université de Savoie – Université Joseph Fourier - Grenoble I Maison des Géosciences 1381 Rue de la piscine - BP 53 38041 GRENOBLE CEDEX 9 France
3 : Centre Technique de l'Equipement [Nice] (LCPC/CETE)
http://www.cete-aix.fr/imgarea/plaquetteLABO_webv2.pdf
CETE Méditerranée Laboratoire régional de Nice 56, bd Stalingrad 06359 Nice - cedex 4 France
4 : INRIA Sophia Antipolis (INRIA Sophia Antipolis)
http://www-sop.inria.fr/
INRIA 2004 route des Lucioles BP 93 06902 Sophia Antipolis France

Références bibliographiques

Type de publication : Articles dans des revues avec comité de lecture
domaine :
Planète et Univers/Sciences de la Terre/Géophysique

Physique/Physique/Géophysique

Sciences de l'environnement/Milieux et Changements globaux
Code Bibliographique ADS : 2010GeoJI.183..941E
titre : An hp-adaptive discontinuous Galerkin finite-element method for 3-D elastic wave modelling
résumé : We present a discontinuous Galerkin finite-element method (DG-FEM) formulation with Convolutional Perfectly Matched Layer (CPML) absorbing boundary condition for 3-D elastic seismic wave modelling. This method makes use of unstructured tetrahedral meshes locally refined according to the medium properties (h-adaptivity), and of approximation orders that can change from one element to another according to an adequate criterion (p-adaptivity). These two features allow us to significantly reduce the computational cost of the simulations. Moreover, we have designed an efficient CPML absorbing boundary condition, both in terms of absorption and computational cost, by combining approximation orders in the numerical domain. A quadratic interpolation is typically used in the medium to obtain the required accuracy, while lower approximation orders are used in the CPMLs to reduce the total computational cost and to obtain a well-balanced workload over the processors. While the efficiency of DG-FEMs have been largely demonstrated for high approximation orders, we favour the use of low approximation orders as they are more appropriate to the applications we are interested in. In particular, we address the issues of seismic modelling and seismic imaging in cases of complex geological structures that require a fine discretization of the medium. We illustrate the efficiency of our approach within the framework of the EUROSEISTEST verification and validation project, which is designed to compare high-frequency (up to 4 Hz) numerical predictions of ground motion in the Volvi basin (Greece). Through the tetrahedral meshing, we have achieved fine discretization of the basin, which appears to be a sine qua non condition for accurate computation of surface waves diffracted at the basin edges. We compare our results with predictions computed with the spectral element method (SEM), and demonstrate that our method yields the same level of accuracy with computation times of the same order of magnitude.
langue du texte
intégral : Anglais
DOI : 10.1111/J.1365-246X.2010.04764.X
journal :

Geophysical Journal International

Publisher Oxford University Press (OUP): Policy P - Oxford Open Option A

ISSN 0956-540X (eISSN : 1365-246X)
Audience : internationale
date de publication : 11/2010
volume : 183
page, identifiant, ... : 941-962
mots-clés : Surface waves and free oscillations – Site effects – Computational seismology – Wave propagation
projet(s), collaboration(s) : CEA/CASHIMA
contrat, financement : BP, CGG-VERITAS, EXXON MOBIL, SHELL and TOTAL

insu-00565022, version 1
http://hal-insu.archives-ouvertes.fr/insu-00565022
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Contributeur : Pascale Talour <>
Soumis le : Jeudi 10 Février 2011, 17:26:37
Dernière modification le : Vendredi 9 Décembre 2011, 14:54:00

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Code Bibliographique ADS : 2010GeoJI.183..941E

DOI : 10.1111/J.1365-246X.2010.04764.X

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%% insu-00565022, version 1
%% http://hal-insu.archives-ouvertes.fr/insu-00565022
@article{etienne:insu-00565022,
    hal_id = {insu-00565022},
    url = {http://hal-insu.archives-ouvertes.fr/insu-00565022},
    title = {{An hp-adaptive discontinuous Galerkin finite-element method for 3-D elastic wave modelling}},
    author = {Etienne, V. and Chaljub, E. and Virieux, J. and Glinsky, N.},
    abstract = {{We present a discontinuous Galerkin finite-element method (DG-FEM) formulation with Convolutional Perfectly Matched Layer (CPML) absorbing boundary condition for 3-D elastic seismic wave modelling. This method makes use of unstructured tetrahedral meshes locally refined according to the medium properties (h-adaptivity), and of approximation orders that can change from one element to another according to an adequate criterion (p-adaptivity). These two features allow us to significantly reduce the computational cost of the simulations. Moreover, we have designed an efficient CPML absorbing boundary condition, both in terms of absorption and computational cost, by combining approximation orders in the numerical domain. A quadratic interpolation is typically used in the medium to obtain the required accuracy, while lower approximation orders are used in the CPMLs to reduce the total computational cost and to obtain a well-balanced workload over the processors. While the efficiency of DG-FEMs have been largely demonstrated for high approximation orders, we favour the use of low approximation orders as they are more appropriate to the applications we are interested in. In particular, we address the issues of seismic modelling and seismic imaging in cases of complex geological structures that require a fine discretization of the medium. We illustrate the efficiency of our approach within the framework of the EUROSEISTEST verification and validation project, which is designed to compare high-frequency (up to 4 Hz) numerical predictions of ground motion in the Volvi basin (Greece). Through the tetrahedral meshing, we have achieved fine discretization of the basin, which appears to be a sine qua non condition for accurate computation of surface waves diffracted at the basin edges. We compare our results with predictions computed with the spectral element method (SEM), and demonstrate that our method yields the same level of accuracy with computation times of the same order of magnitude.}},
    keywords = {Surface waves and free oscillations;Site effects;Computational seismology;Wave propagation;},
    language = {Anglais},
    affiliation = {G{\'e}oazur - GEOAZUR , Laboratoire de g{\'e}ophysique interne et tectonophysique - LGIT , Centre Technique de l'Equipement [Nice] - LCPC/CETE , INRIA Sophia Antipolis - INRIA Sophia Antipolis},
    pages = {941-962},
    journal = {Geophysical Journal International},
    volume = {183},
    note = {BP, CGG-VERITAS, EXXON MOBIL, SHELL and TOTAL },
    audience = {internationale },
    collaboration = {CEA/CASHIMA },
    doi = {10.1111/J.1365-246X.2010.04764.X },
    year = {2010},
    month = Nov,
}

%F insu-00565022, version 1
%0 Journal Article
%U http://hal-insu.archives-ouvertes.fr/insu-00565022
%2 SDU:STU:GP;PHYS:PHYS:PHYS_GEO-PH;SDE:MCG
%T An hp-adaptive discontinuous Galerkin finite-element method for 3-D elastic wave modelling
%A Etienne, V.
%A Chaljub, E.
%A Virieux, J.
%A Glinsky, N.
%+ Géoazur - GEOAZUR , Laboratoire de géophysique interne et tectonophysique - LGIT , Centre Technique de l'Equipement [Nice] - LCPC/CETE , INRIA Sophia Antipolis - INRIA Sophia Antipolis
%X We present a discontinuous Galerkin finite-element method (DG-FEM) formulation with Convolutional Perfectly Matched Layer (CPML) absorbing boundary condition for 3-D elastic seismic wave modelling. This method makes use of unstructured tetrahedral meshes locally refined according to the medium properties (h-adaptivity), and of approximation orders that can change from one element to another according to an adequate criterion (p-adaptivity). These two features allow us to significantly reduce the computational cost of the simulations. Moreover, we have designed an efficient CPML absorbing boundary condition, both in terms of absorption and computational cost, by combining approximation orders in the numerical domain. A quadratic interpolation is typically used in the medium to obtain the required accuracy, while lower approximation orders are used in the CPMLs to reduce the total computational cost and to obtain a well-balanced workload over the processors. While the efficiency of DG-FEMs have been largely demonstrated for high approximation orders, we favour the use of low approximation orders as they are more appropriate to the applications we are interested in. In particular, we address the issues of seismic modelling and seismic imaging in cases of complex geological structures that require a fine discretization of the medium. We illustrate the efficiency of our approach within the framework of the EUROSEISTEST verification and validation project, which is designed to compare high-frequency (up to 4 Hz) numerical predictions of ground motion in the Volvi basin (Greece). Through the tetrahedral meshing, we have achieved fine discretization of the basin, which appears to be a sine qua non condition for accurate computation of surface waves diffracted at the basin edges. We compare our results with predictions computed with the spectral element method (SEM), and demonstrate that our method yields the same level of accuracy with computation times of the same order of magnitude.
%G Anglais
%R 10.1111/J.1365-246X.2010.04764.X
%J Geophysical Journal International
%2 internationale
%8 2010-11-00
%V 183
%P 941-962
%K Surface waves and free oscillations;Site effects;Computational seismology;Wave propagation;
%Z CEA/CASHIMA
%Z BP, CGG-VERITAS, EXXON MOBIL, SHELL and TOTAL

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Geophysical Journal International
Publisher	Oxford University Press (OUP): Policy P - Oxford Open Option A
ISSN	0956-540X (eISSN : 1365-246X)