Convergence of frozen Gaussian approximation for high-frequency wave propagation

DOI10.1002/cpa.21384zbMath1387.35400arXiv1012.5055OpenAlexW2059763171MaRDI QIDQ2885496

Xu Yang, Jian-feng Lu

Publication date: 23 May 2012

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.5055

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) First-order hyperbolic systems (35L40)

Related Items (21)

Classical limit for the varying-mass Schrödinger equation with random inhomogeneities ⋮ Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime ⋮ Frozen Gaussian approximation-based artificial boundary conditions for one-dimensional nonlinear Schrödinger equation in the semiclassical regime ⋮ Frozen Gaussian approximation for 3D seismic tomography ⋮ Optimal error estimate of the extended-WKB approximation to the high frequency wave-type equation in the semi-classical regime ⋮ Frozen Gaussian approximation-based two-level methods for multi-frequency Schrödinger equation ⋮ Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene ⋮ Error estimates for Gaussian beam methods applied to symmetric strictly hyperbolic systems ⋮ Seismic Tomography with Random Batch Gradient Reconstruction ⋮ A Spectral Algorithm for the Time-Dependent Kohn--Sham Equations: Accurately Treating External Potentials Based on Frozen Gaussian Approximations ⋮ Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs ⋮ A Diabatic Surface Hopping Algorithm Based on Time Dependent Perturbation Theory and Semiclassical Analysis ⋮ Symplectic coarse-grained classical and semclassical evolution of subsystems: New theoretical approach ⋮ Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms ⋮ The Gaussian Wave Packet Transform for the Semi-Classical Schrödinger Equation with Vector Potentials ⋮ The Eulerian Gaussian beam method for high frequency wave propagation in the reduced momentum space ⋮ A wavefront-based Gaussian beam method for computing high frequency wave propagation problems ⋮ A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion ⋮ Gauge-Invariant Frozen Gaussian Approximation Method for the Schrödinger Equation with Periodic Potentials ⋮ A multi-scale Gaussian beam parametrix for the wave equation: the Dirichlet boundary value problem ⋮ Frozen Gaussian Approximation for the Dirac Equation in Semiclassical Regime

Cites Work

• Frozen Gaussian approximation for high frequency wave propagation
• Taylor expansion and discretization errors in Gaussian beam superposition
• A mathematical justification for the Herman-Kluk propagator
• A new method of computation of wave fields using Gaussian beams
• Gaussian beams summation for the wave equation in a convex domain
• ON THE HERMAN–KLUK SEMICLASSICAL APPROXIMATION
• Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation
• Recovery of High Frequency Wave Fields for the Acoustic Wave Equation
• Recovery of High Frequency Wave Fields from Phase Space–Based Measurements
• Computational high frequency wave propagation
• An introduction to semiclassical and microlocal analysis
• Unnamed Item
• Unnamed Item

This page was built for publication: Convergence of frozen Gaussian approximation for high-frequency wave propagation