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Journal of Scientific Computing

Erschienen in:

01.02.2015

Asymptotic-Preserving Exponential Methods for the Quantum Boltzmann Equation with High-Order Accuracy

verfasst von: Jingwei Hu, Qin Li, Lorenzo Pareschi

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2015

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Abstract

In this paper we develop high order asymptotic preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi (J Comput Phys 259:402–420, 2014) where asymptotic preserving exponential Runge–Kutta methods for the classical inhomogeneous Boltzmann equation were constructed. A major difficulty here is related to the non Gaussian steady states characterizing the quantum kinetic behavior. We show that the proposed schemes achieve high-order accuracy uniformly in time for all Planck constants ranging from classical regime to quantum regime, and all Knudsen number ranging from kinetic regime to fluid regime. Computational results are presented for both Bose gas and Fermi gas.

Vorheriger Artikel Operator Bounds and Time Step Conditions for the DG and Central DG Methods

Nächster Artikel A New Framework of GPU-Accelerated Spectral Solvers: Collocation and Glerkin Methods for Systems of Coupled Elliptic Equations

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Titel: Asymptotic-Preserving Exponential Methods for the Quantum Boltzmann Equation with High-Order Accuracy
verfasst von: Jingwei Hu
Qin Li
Lorenzo Pareschi
Publikationsdatum: 01.02.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2015
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9869-2

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