• 论文 •

### 矩阵形式二次修正Maxwell-Dirac系统的多尺度算法

1. 1. 中国科学院大学, 北京 100190;
2. 中国科学院数学与系统科学研究院计算数学与科学工程计算研究所, 北京 100190;
3. 中国科学院数学与系统科学研究院计算数学与科学工程计算研究所, 科学与工程计算国家重点实验室, 国家数学与交叉科学中心, 北京 100190
• 收稿日期:2019-01-23 出版日期:2019-12-15 发布日期:2019-11-16
• 通讯作者: 曹礼群,Email:clq@lsec.cc.ac.cn.
• 基金资助:

国家自然科学基金重点项目（91330202）、面上项目（11571353）资助.

Fu Yaoyao, Cao Liqun. THE MULTISCALE ALGORITHMS FOR THE MAXWELL-DIRAC SYSTEM IN MATRIX FORM WITH QUADRATIC CORRECTION[J]. Mathematica Numerica Sinica, 2019, 41(4): 419-439.

### THE MULTISCALE ALGORITHMS FOR THE MAXWELL-DIRAC SYSTEM IN MATRIX FORM WITH QUADRATIC CORRECTION

Fu Yaoyao1,2, Cao Liqun1,3

1. 1. University of Chinese Academy of Sciences, Beijing 100190, China;
2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
3. LSEC, NCMIS, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
• Received:2019-01-23 Online:2019-12-15 Published:2019-11-16

The Maxwell-Dirac system with quadratic correction has a wide applications in materials science such as topological insulators, graphene, superconductors and so on. In this paper, we first present the Dirac equation in matrix form with quadratic correction. Combining the Maxwell's equations, we present the homogenization method and the multiscale asymptotic method for the modified Maxwell-Dirac system in matrix form with rapidly oscillating discontinuous coefficients in a bounded Lipschitz convex domain under the Weyl gauge. Based on the multiscale asymptotic expansions of the solution of the Maxwell-Dirac system, by using the Crank-Nicolson finite difference method and the adaptive edge element method, we developed the multiscale algorithms for solving the Maxwell-Dirac system with rapidly oscillating discontinuous coefficients. Numerical examples are then carried out to validate the method presented in this paper.

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