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

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.