We consider time-dependent (linear and nonlinear) Schrödinger equations in a
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …

This paper introduces a wavepacket-transform-based Gaussian beam method for solving
the Schrödinger equation. We focus on addressing two computational issues of the …

The solution to the Schrödinger equation is highly oscillatory when the rescaled Planck
constant ε is small in the semiclassical regime. A direct numerical simulation requires the …

In some applications, it is reasonable to assume that geodesics (rays) have a consistent
orientation so that the Helmholtz equation may be viewed as an evolution equation in one of …

Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial
differential equations, concentrated on a single curve through the physical domain. They can …

We introduce a new multiscale Gaussian beam method for the numerical solution of the
wave equation with smooth variable coefficients. The first computational question addressed …

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 …

The frozen Gaussian approximation provides a highly efficient computational method for
high‐frequency wave propagation. The derivation of the method is based on asymptotic …

The Dirac equation is an important model in relativistic quantum mechanics. In the semi-
classical regime $\epsilon\ll1 $, even a spatially spectrally accurate time splitting method\cite …

In some applications, it is reasonable to assume that geodesics (rays) have a consistent
orientation so that the Helmholtz equation can be viewed as an evolution equation in one of …