Error estimates for Gaussian beam methods applied to symmetric strictly hyperbolic systems

Liu, Hailiang; Pryporov, Maksym

doi:10.1016/j.wavemoti.2017.05.004

Cited by 3 publications

(1 citation statement)

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“…In this paper we investigate issues related to the accuracy of Gaussian beam approximations to high frequency wave propagation. This is related to recent results on Gaussian beam methods in [5][6][7][8][9][10][11]13]. Our model equation is the acoustic wave equation where c(x) is a positive smooth function.…”

Section: Introductionsupporting

confidence: 57%

General superpositions of Gaussian beams and propagation errors

2019

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Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to PDEs. We present a superposition of Gaussian beams over an arbitrary bounded set of dimension m in phase space, and show that the tools recently developed in [ H. Liu, O. Runborg, and N. M. Tanushev, Math. Comp., 82: 919-952, 2013] can be applied to obtain the propagation error of order k 1− N, where N is the order of beams and d is the spatial dimension. Moreover, we study the sharpness of this estimate in examples.2000 Mathematics Subject Classification. Primary 35L05, 35A35, 41A60.

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Section: Introductionsupporting

confidence: 57%

General superpositions of Gaussian beams and propagation errors

2019

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A Surface Hopping Gaussian Beam Method for High-Dimensional Transport Systems

Cai¹,

Lu²

2018

SIAM J. Sci. Comput.

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We propose a surface hopping Gaussian beam method to numerically solve a class of high frequency linear transport systems in high spatial dimensions, based on asymptotic analysis. The stochastic surface hopping is combined with Gaussian beam method to deal with the multiple characteristic directions of the transport system in high dimensions. The Monte Carlo nature of the proposed algorithm makes it easy for parallel implementations. We validate the performance of the algorithms for applications on the quantum-classical Liouville equations.

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