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Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers

Published online by Cambridge University Press:  20 August 2015

Qin Sheng  and
Hai-Wei Sun
Qin Sheng*
Affiliation:
Center for Astrophysics, Space Physics and Engineering Research, Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA
Hai-Wei Sun*
Affiliation:
Department of Mathematics, University of Macau, Macao
*
Corresponding author.Email:qin_sheng@baylor.edu
Email:HSun@umac.mo
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Abstract

This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number. Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense. Simulated examples are given to illustrate the conclusion.

Keywords

65M0665M1265F3515A12Paraxial equationhighly oscillatory problemseikonal splittingasymptotic stabilitymatrix eigenvaluesspectral radius
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 4 , October 2012 , pp. 1275 - 1292
Copyright
Copyright © Global Science Press Limited 2012

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