Convergence of frozen Gaussian approximation for high frequency wave propagation

TL;DR

This paper establishes the rigorous convergence of the frozen Gaussian approximation method for high frequency wave propagation in hyperbolic systems and introduces higher order variants for improved accuracy.

Contribution

It provides the first rigorous convergence proof for the frozen Gaussian approximation in general hyperbolic systems and develops higher order methods.

Findings

Proved convergence of frozen Gaussian approximation for hyperbolic systems.

Developed higher order frozen Gaussian approximation methods.

Enhanced computational efficiency for high frequency wave simulations.

Abstract

The frozen Gaussian approximation provides a highly efficient computational method for high frequency wave propagation. The derivation of the method is based on asymptotic analysis. In this paper, for general linear strictly hyperbolic system, we establish the rigorous convergence result for frozen Gaussian approximation. As a byproduct, higher order frozen Gaussian approximation is developed.