Frozen Gaussian approximation for high frequency wave propagation

TL;DR

The paper introduces the frozen Gaussian approximation, a computational method for high frequency wave propagation that remains accurate near caustics and improves upon Gaussian beam methods.

Contribution

It presents a novel approximation technique that overcomes limitations of geometric optics and Gaussian beam methods, enhancing accuracy and robustness in wave simulations.

Findings

Performs well near caustics

Handles Gaussian beam spreading effectively

Provides accurate solutions in high frequency regimes

Abstract

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 not only overcomes the drawback of beam spreading but also improves the asymptotic accuracy. 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.