Pseudo-spectral solution of nonlinear Schro¨dinger equations
Journal of Computational Physics
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
Journal of Computational Physics
Journal of Computational Physics
Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
Journal of Computational Physics
Gaussian beam decomposition of high frequency wave fields
Journal of Computational Physics
Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation
Journal of Computational Physics
Fast multiscale Gaussian beam methods for wave equations in bounded convex domains
Journal of Computational Physics
An Eulerian method for computing the coherent ergodic partition of continuous dynamical systems
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrodinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.