Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids
- Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, One Bear Place, Waco, TX 76798-7328 (United States)
- Department of Mathematics, University of Macau (Macao)
This study concerns the asymptotic stability of an eikonal, or ray, transformation based Peaceman–Rachford splitting method for solving the paraxial Helmholtz equation with high wave numbers. Arbitrary nonuniform grids are considered in transverse and beam propagation directions. The differential equation targeted has been used for modeling propagations of high intensity laser pulses over a long distance without diffractions. Self-focusing of high intensity beams may be balanced with the de-focusing effect of created ionized plasma channel in the situation, and applications of grid adaptations are frequently essential. It is shown rigorously that the fully discretized oscillation-free decomposition method on arbitrary adaptive grids is asymptotically stable with a stability index one. Simulation experiments are carried out to illustrate our concern and conclusions.
- OSTI ID:
- 22622212
- Journal Information:
- Journal of Computational Physics, Vol. 325; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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