scholarly journals Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number

2009 ◽  
Vol 47 (4) ◽  
pp. 2872-2896 ◽  
Author(s):  
Xiaobing Feng ◽  
Haijun Wu
Keyword(s):  
Helmholtz Equation ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Wave Number ◽  
Galerkin Methods ◽  
Large Wave ◽  
Large Wave Number

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

2012 ◽  
Vol 12 (4) ◽  
pp. 1275-1292 ◽  
Author(s):  
Qin Sheng ◽  
Hai-Wei Sun
Keyword(s):  
Helmholtz Equation ◽  
Numerical Stability ◽  
Splitting Method ◽  
Computational Procedure ◽  
Matrix Analysis ◽  
Wave Number ◽  
Large Wave ◽  
High Wave ◽  
Wave Numbers ◽  
Large Wave Number

AbstractThis 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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