A MICRO-MACRO METHOD FOR A KINETIC GRAPHENE MODEL IN ONE SPACE DIMENSION

被引：0
|
作者：
Crouseilles, Nicolas [1 ,2 ]
Jin, Shi [3 ,4 ]
Lemou, Mohammed [5 ,6 ]
Mehats, Florian [6 ,7 ]
机构：
[1] Univ Rennes, INRIA, MINGuS Team, F-35042 Rennes, France
[2] IRMAR, F-35042 Rennes, France
[3] Shanghai Jiao Tong Univ, Sch Math Sci, Inst Nat Sci, MOE LSEC, Shanghai 200240, Peoples R China
[4] Shanghai Jiao Tong Univ, SHL MAC, Shanghai 200240, Peoples R China
[5] Univ Rennes, CNRS, IRMAR, F-35042 Rennes, France
[6] Univ Rennes, Inria MINGuS Team, F-35042 Rennes, France
[7] Univ Rennes, IRMAR, F-35042 Rennes, France
来源：
MULTISCALE MODELING & SIMULATION | 2020年 / 18卷 / 01期
关键词：
phase-space models; highly oscillatory momentum-space-time; uniformly accurate numerical method; micro-macro decomposition; NUMERICAL SCHEMES; EQUATION; TRANSPORT;
D O I：
10.1137/18M1173770
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we propose a numerical method solving the one space dimensional semiclassical kinetic graphene model introduced in [O. Morandi and F. Schurrer, T. 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.
引用
收藏
页码：444 / 474
页数：31
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