@Article{cmes.2010.056.017,
AUTHOR = {R.  Martin, D.  Komatitsch, S. D.  Gedney, E.  Bruthiaux},
TITLE = {A High-Order Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADE-PML)},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {56},
YEAR = {2010},
NUMBER = {1},
PAGES = {17--42},
URL = {http://www.techscience.com/CMES/v56n1/25463},
ISSN = {1526-1506},
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.},
DOI = {10.3970/cmes.2010.056.017}
}