Open Access

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)

by R. Martin¹, D. Komatitsch¹, S. D. Gedney³, E. Bruthiaux¹

1 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
2 Institut universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France
3 Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY40506-0046, USA. E-mail: gedney@engr.uky.edu
4 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

Computer Modeling in Engineering & Sciences 2010, 56(1), 17-42. https://doi.org/10.3970/cmes.2010.056.017

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.

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