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Exponential splitting for n-dimensional paraxial Helmholtz equation with high wavenumbers
Sheng,Qin1; Sun,Hai Wei2
Source PublicationComputers and Mathematics with Applications

This paper explores applications of the exponential splitting method for approximating highly oscillatory solutions of the n-dimensional paraxial Helmholtz equation. An eikonal transformation is introduced for oscillation-free platforms and matrix operator decompositions. It is found that the sequential, parallel and combined exponential splitting formulas possess not only anticipated algorithmic simplicity and efficiency, but also the accuracy and asymptotic stability required for highly oscillatory wave computations.

KeywordAsymptotic Stability Eikonal Transformation Exponential Splitting High Oscillations High Wavenumber Paraxial Helmholtz Equation
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WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000345475600018
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Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Affiliation1.Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University,Waco,76798-7328,United States
2.Department of Mathematics, University of Macau,Macao
Recommended Citation
GB/T 7714
Sheng,Qin,Sun,Hai Wei. Exponential splitting for n-dimensional paraxial Helmholtz equation with high wavenumbers[J]. Computers and Mathematics with Applications,2014,68(10):1341-1354.
APA Sheng,Qin,&Sun,Hai Wei.(2014).Exponential splitting for n-dimensional paraxial Helmholtz equation with high wavenumbers.Computers and Mathematics with Applications,68(10),1341-1354.
MLA Sheng,Qin,et al."Exponential splitting for n-dimensional paraxial Helmholtz equation with high wavenumbers".Computers and Mathematics with Applications 68.10(2014):1341-1354.
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