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

页码：444 / 474

页数：31

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