Communications in Mathematical Sciences

Volume 9 (2011)

Number 3

Frozen Gaussian approximation for high frequency wave propagation

Pages: 663 – 683



Jianfeng Lu (Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York)

Xu Yang (Program in Applied and Computational Mathematics, Princeton University)


We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool based on the asymptotic analysis on the phase plane. Compared to geometric optics, it provides a valid solution around caustics. Compared to the Gaussian beam method, it overcomes the drawback of beam spreading. We give several numerical examples to verify that the frozen Gaussian approximation performs well in the presence of caustics and when the Gaussian beam spreads. Moreover, it is observed numerically that the frozen Gaussian approximation exhibits better accuracy than the Gaussian beam method.


High frequency wave propagation, Frozen Gaussian approximation, wave equation, phase plane analysis, asymptotics

2010 Mathematics Subject Classification

35L05, 65Mxx, 81Q20

Published 11 March 2011