Higher-Order Numerical Schemes and Operator Splitting for Solving 3D Paraxial Wave Equations in Heterogeneous Media

Eliane Bécache 1 Francis Collino 1 Patrick Joly 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 investigate numerical schemes for solving 3D paraxial wave equations that are compatible with the use of splitting methods without losing accuracy. The novelty of these paraxial equations (introduced in \cite{col.jol:2}) compared with classical alternate directions methods is to use more than the two usual cross-line and in-line directions for the splitting. It gives rise to a series of 2D extrapolations in each direction of splitting. Propagation along depth is done with a higher-order method based on a conservative Runge Kutta method. The discretization along the lateral variable is done using higher-order finite difference variational schemes. We present a detailed plane wave analysis in a homogeneous medium that leads to a classification of several particular schemes with respect to the numerical dispersion they generate. The dispersion an= alysis extended to 3D helps chosing the «best» coefficients of the extrapolati= on operators on the dispersion point of view. We conclude with numerical experiments in 2D as well as in 3D homogeneous and heterogeneous media.
Type de document :
Rapport
[Research Report] RR-3497, INRIA. 1998
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https://hal.inria.fr/inria-00073188
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Soumis le : mercredi 24 mai 2006 - 12:06:30
Dernière modification le : vendredi 25 mai 2018 - 12:02:03
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Eliane Bécache, Francis Collino, Patrick Joly. Higher-Order Numerical Schemes and Operator Splitting for Solving 3D Paraxial Wave Equations in Heterogeneous Media. [Research Report] RR-3497, INRIA. 1998. 〈inria-00073188〉

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