TY - EJOU
AU - Martin, R.
AU - Komatitsch, D.
AU - Gedney, S. D.
AU - Bruthiaux, E.
TI - A High-Order Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADE-PML)
T2 - Computer Modeling in Engineering \& Sciences
PY - 2010
VL - 56
IS - 1
SN - 1526-1506
AB - 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.
KW - Finite differences
KW - FDTD
KW - high-order
KW - Perfectly Matched Layer (PML)
KW - seismic wave propagation
KW - absorbing conditions
KW - Auxiliary Differential Equations (ADE)
DO - 10.3970/cmes.2010.056.017