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Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids
Sheng,Qin1; Sun,Hai wei2
2016-10-10
Source PublicationJournal of Computational Physics
ISSN10902716 00219991
Volume325Pages:259-271
Abstract

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.

KeywordAdaptive Grids Asymptotic Stability Eikonal Transformation High Oscillations Paraxial Wave Approximations Splitting Methods
DOI10.1016/j.jcp.2016.08.040
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000384077600014
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Affiliation1.Department of MathematicsCenter for AstrophysicsSpace Physics and Engineering ResearchBaylor University,Waco,76798-7328,United States
2.Department of MathematicsUniversity of Macau,Macao
Recommended Citation
GB/T 7714
Sheng,Qin,Sun,Hai wei. Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids[J]. Journal of Computational Physics,2016,325:259-271.
APA Sheng,Qin,&Sun,Hai wei.(2016).Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids.Journal of Computational Physics,325,259-271.
MLA Sheng,Qin,et al."Stability of a modified Peaceman–Rachford method for the paraxial Helmholtz equation on adaptive grids".Journal of Computational Physics 325(2016):259-271.
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