Frozen gaussian approximation for general linear strictly hyperbolic systems: Formulation and eulerian methods
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2012-09-07
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The frozen Gaussian approximation, proposed in [J. Lu and X. Yang, Commun. Math. Sci., 9 (2011), pp. 663-683], is an efficient computational tool for high frequency wave propagation. We continue in this paper the development of frozen Gaussian approximation. The frozen Gaussian approximation is extended to general linear strictly hyperbolic systems. Eulerian methods based on frozen Gaussian approximation are developed to overcome the divergence problem of Lagrangian methods. The proposed Eulerian methods can also be used for the Herman-Kluk propagator in quantum mechanics. Numerical examples verify the performance of the proposed methods. © 2012 Society for Industrial and Applied Mathematics.
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Lu, J, and X Yang (2012). Frozen gaussian approximation for general linear strictly hyperbolic systems: Formulation and eulerian methods. Multiscale Modeling and Simulation, 10(2). pp. 451–472. 10.1137/10081068X Retrieved from https://hdl.handle.net/10161/14090.
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Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
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