Vol.56, No.1, 2010, pp.17-42, doi:10.3970/cmes.2010.056.017
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ARTICLE
A High-Order Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADE-PML)
  • R. Martin1, D. Komatitsch1,2, S. D. Gedney3, E. Bruthiaux1,4
Université de Pau et des Pays de l’Adour, CNRS and INRIA Magique-3D. Laboratoire de Modéli-sation et Imagerie en Géosciences UMR 5212, Avenue de l’Université, 64013 Pau cedex, France. E-mail: roland.martin@univ-pau.fr, dimitri.komatitsch@univ-pau.fr
Institut universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France
Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY40506-0046, USA. E-mail: gedney@engr.uky.edu
École Normale Supérieure de Lyon, Laboratoire de Sciences de la Terre, UMR 5570, 46 alléed’Italie, 69007 Lyon, France. E-mail: emilien.bruthiaux@ens-lyon.fr
Abstract
Unsplit convolutional perfectly matched layers (CPML) for the velocity and stress formulation of the seismic wave equation are classically computed based on a second-order finite-difference time scheme. However it is often of interest to increase the order of the time-stepping scheme in order to increase the accuracy of the algorithm. This is important for instance in the case of very long simulations. We study how to define and implement a new unsplit non-convolutional PML called the Auxiliary Differential Equation PML (ADE-PML), based on a high-order Runge-Kutta time-stepping scheme and optimized at grazing incidence. We demonstrate that when a second-order time-stepping scheme is used the convolutional PML can be derived from that more general non-convolutional ADE-PML formulation, but that this new approach can be generalized to high-order schemes in time, which implies that it can be made more accurate. We also show that the ADE-PML formulation is numerically stable up to 100,000 time steps.
Keywords
Finite differences, FDTD, high-order, Perfectly Matched Layer (PML), seismic wave propagation, absorbing conditions, Auxiliary Differential Equations (ADE).
Cite This Article
Martin, R., Komatitsch, D., Gedney, S. D., Bruthiaux, E. (2010). A High-Order Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADE-PML). CMES-Computer Modeling in Engineering & Sciences, 56(1), 17–42.
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