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Status已發表Published
Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids
Sheng, Q; Sun, H. W.
2016-11-01
Source PublicationJournal of Compuational Physics
ISSN0021-9991
Pages259-271
AbstractThis study concerns the asymptotic stability of an eikonal, or ray, transformation basedPeaceman–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.
KeywordParaxial wave approximations High oscillations Asymptotic stability Eikonal transformation Splitting methods Adaptive grids
URLView the original
Language英語English
The Source to ArticlePB_Publication
PUB ID25838
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorSheng, Q
Recommended Citation
GB/T 7714
Sheng, Q,Sun, H. W.. Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids[J]. Journal of Compuational Physics,2016:259-271.
APA Sheng, Q,&Sun, H. W..(2016).Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids.Journal of Compuational Physics,259-271.
MLA Sheng, Q,et al."Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids".Journal of Compuational Physics (2016):259-271.
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