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Volume 12, Issue 4
Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers

Qin Sheng & Hai-Wei Sun

DOI: 10.4208/cicp.100811.090112a

Commun. Comput. Phys., 12 (2012), pp. 1275-1292.

Published online: 2012-12

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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. 

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@Article{CiCP-12-1275, author = {}, title = {Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {4}, pages = {1275--1292}, 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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.100811.090112a}, url = {http://global-sci.org/intro/article_detail/cicp/7334.html} }
TY - JOUR T1 - Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers JO - Communications in Computational Physics VL - 4 SP - 1275 EP - 1292 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.100811.090112a UR - https://global-sci.org/intro/article_detail/cicp/7334.html KW - AB -

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. 

Qin Sheng & Hai-Wei Sun. (2020). Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers. Communications in Computational Physics. 12 (4). 1275-1292. doi:10.4208/cicp.100811.090112a
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