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A Micro-Macro Method for a Kinetic Graphene Model in One Space Dimension
Multiscale Modeling and Simulation ( IF 1.9 ) Pub Date : 2020-03-24 , DOI: 10.1137/18m1173770
Nicolas Crouseilles , Shi Jin , Mohammed Lemou , Florian Méhats

Multiscale Modeling &Simulation, Volume 18, Issue 1, Page 444-474, January 2020.
In this paper, we propose a numerical method solving the one space dimensional semiclassical kinetic graphene model introduced in [O. Morandi and F. Schürrer, J. Phys. A, 44 (2012), pp. 265--301] involving fast oscillations in time, space, and momentum. This method can numerically capture the oscillatory space-time quantum solution pointwisely even without numerically resolving the frequency. We prove that the underlying micro-macro equations have smooth (up to a certain order of derivatives) solutions with respect to the frequency, and then we prove the uniform accuracy of the numerical discretization for a scalar model equation exhibiting the same oscillatory behavior. Numerical experiments verify the theory.


中文翻译:

一维空间动力学石墨烯模型的微宏方法

《多尺度建模与仿真》,第18卷,第1期,第444-474页,2020
年1月。在本文中,我们提出了一种数值方法,用于解决[O. Chem。Chem。,1989,1,1,3,4,5,6,5,6,6,8,8,8,8,8,9,8,8,9,8,9,8,9,8,9,8,9,8,8,9,8,8,9,8,9,9,8,9,8,8,9,8,8,8,9,8,9,8,9,8,9 。Morandi和F.Schürrer,《物理学报》A,44(2012),第265--301页],涉及时间,空间和动量的快速振荡。即使没有数值解析频率,该方法也可以逐点数值捕捉振荡时空量子解。我们证明了潜在的微观宏方程具有相对于频率的光滑(至一定阶数的导数)解,然后证明了表现出相同振动行为的标量模型方程的数值离散化的一致精度。数值实验验证了这一理论。
更新日期:2020-03-24
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