Recovery of High Frequency Wave Fields from Phase Space–Based Measurements

DOI10.1137/090756909zbMath1221.35031arXiv0904.3776OpenAlexW2134228643MaRDI QIDQ3567050

J. V. Ralston, Hai-liang Liu

Publication date: 10 June 2010

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.3776

zbMATH Keywords

Gaussian beamscomputations in phase spacenew level set method

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Theoretical approximation in context of PDEs (35A35) Singularity in context of PDEs (35A21)

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Convergence of frozen Gaussian approximation for high-frequency wave propagation ⋮ Frozen Gaussian approximation-based artificial boundary conditions for one-dimensional nonlinear Schrödinger equation in the semiclassical regime ⋮ Gabor frames of Gaussian beams for the Schrödinger equation ⋮ Optimal error estimate of the extended-WKB approximation to the high frequency wave-type equation in the semi-classical regime ⋮ Error estimates for Gaussian beam methods applied to symmetric strictly hyperbolic systems ⋮ Taylor expansion and discretization errors in Gaussian beam superposition ⋮ Stochastic regularity of a quadratic observable of high-frequency waves ⋮ Error estimates for Gaussian beam superpositions ⋮ 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 ⋮ General superpositions of Gaussian beams and propagation errors ⋮ Mathematical and computational methods for semiclassical Schrödinger equations ⋮ Asymptotic approximations for the phase space Schrödinger equation

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