删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

矩阵形式二次修正Maxwell-Dirac系统的多尺度算法

本站小编 Free考研考试/2021-12-27

付姚姚1,2, 曹礼群1,3
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.


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

Fu Yaoyao1,2, Cao Liqun1,3
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:2019-01-23Online:2019-12-15Published:2019-11-16







摘要



编辑推荐
-->


带二次修正项的Dirac方程在拓扑绝缘体、石墨烯、超导等新材料电磁光特性分析中有着十分广泛的应用.本文工作的创新点有:一是首次提出了矩阵形式带有二次修正项的Dirac方程,它是比较一般的数学框架,涵盖了上述材料体系很多重要的物理模型,具体见附录A;二是针对上述材料体系的电磁响应问题,提出了有界区域Weyl规范下具有周期间断系数矩阵形式带二次修正项Maxwell-Dirac系统的多尺度渐近方法,结合Crank-Nicolson有限差分方法和自适应棱单元方法,发展了一类多尺度算法.数值试验结果验证了多尺度渐近方法的正确性和算法的有效性.
MR(2010)主题分类:
34E05
35B27
65L60

分享此文:


()

[1] Abenda S. Solitary waves for Maxwell-Dirac and Coulomb-Dirac models[C]. Annales de l'Institut Henri Poincare-A Physique Theorique. Paris:Gauthier-Villars, c1983-c1999., 1998, 68(2):229.

[2] Aharonov Y, Bohm D. Significance of electromagnetic potentials in the quantum theory[J]. Physical Review, 1959, 115(3):485-491.

[3] Bao W, Li X G. An efficient and stable numerical method for the Maxwell-Dirac system[J]. Journal of Computational Physics, 2004, 199(2):663-687.

[4] Bechouche P, Mauser N J. (Semi)-nonrelativistic limits of the Dirac equation with external timedependent electromagnetic field[J]. Communications in Mathematical Physics, 1998, 197(2):405-425.

[5] Bensoussan A, Lions J L, Papanicolaou G. Asymptotic Analysis for Periodic Structures[M]. North-Holland, Amsterdam, 1978.

[6] Bernevig B A, Hughes T L. Topological Insulators and Topological Superconductors[M]. Princeton University Press, 2013.

[7] Bjorken J D, Drell S D. Relativistic Quantum Mechanics[M]. McGraw-Hill, 1965.

[8] Cao L Q, Zhang Y, Allegretto W and Lin Y P. Multiscale asymptotic method for Maxwell's equations in composite materials[J]. SIAM Journal on Numerical Analysis, 2010, 47(6):4257-4289.

[9] Chadam J M. Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension[J]. Journal of Functional Analysis, 1973, 13(2):173-184.

[10] Chadam J M, Glassey R T. On the Maxwell-Dirac equations with zero magnetic field and their solution in two space dimensions[J]. Journal of Mathematical Analysis and Applications, 1976, 53(3):495-507.

[11] Cioranescu D, Donato P. An Introduction to Homogenization, volume 17 of Oxford Lecture Series in Mathematics and its Applications[J]. The Clarendon Press Oxford University Press, New York, 2000, 10(31):106-109.

[12] D'Ancona P, Foschi D, Selberg S. Null structure and almost optimal local well-posedness of the Maxwell-Dirac system[J]. American Journal of Mathematics, 2010, 132(3):771-839.

[13] D'Ancona P, Selberg S. Global well-posedness of the Maxwell-Dirac system in two space dimensions[J]. Journal of Functional Analysis, 2011, 260(8):2300-2365.

[14] Esteban M J, Georgiev V, Séré E. Stationary solutions of the Maxwell-Dirac and the KleinGordon-Dirac equations[J]. Calculus of Variations and Partial Differential Equations, 1996, 4(3):265-281.

[15] Esteban M J, Séré E. An overview on linear and nonlinear Dirac equations[J]. Discrete & Continuous Dynamical Systems-A, 2002, 8(2):381-397.

[16] Flato M, Taflin E, Simon J. On global solutions of the Maxwell-Dirac equations[J]. Communications in Mathematical Physics, 1987, 112(1):21-49.

[17] Georgiev V. Small amplitude solutions of the Maxwell-Dirac equations[J]. Indiana University Mathematics Journal, 1991:845-883.

[18] Gerry C, Knight P, Knight P L. Introductory Quantum Optics[M]. Cambridge University Press, 2005.

[19] Glassey R T, Chadam J M. Properties of the solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension[J]. Proceedings of the American Mathematical Society, 1974, 43(2):373-378.

[20] Gross L. The cauchy problem for the coupled maxwell and dirac equations[J]. Communications on Pure & Applied Mathematics, 1966, 19(1):1-15.

[21] Huang Z, Jin S, Markowich P A, et al. A time-splitting spectral scheme for the Maxwell-Dirac system[J]. Journal of Computational Physics, 2005, 208(2):761-789.

[22] Katsnelson M I, Katsnel'son M I. Graphene:Carbon in Two Dimensions[M]. Cambridge University Press, 2012.

[23] Lisi A G. A solitary wave solution of the Maxwell-Dirac equations[J]. Journal of Physics A:Mathematical and General, 1995, 28(18):5385.

[24] McLachlan R I, Quispel G R W. Splitting methods[J]. Acta Numerica, 2002, 11(11):341-434.

[25] Oleinik O A, Shamaev A S, Yosifian G A. Mathematical Problems in Elasticity and Homogenization[M]. North-Holland, Amsterdam, 1992.

[26] Qi X L, Zhang S C. Topological insulators and superconductors[J]. Reviews of Modern Physics, 2011, 83(4):1057.

[27] Raza H. Graphene Nanoelectronics:Metrology, Synthesis, Properties and Applications[M]. Springer Science & Business Media, 2012.

[28] Roche S, Valenzuela S O. Topological Insulators:Fundamentals and Perspectives[M]. John Wiley & Sons, 2015.

[29] Shen S Q. Topological Insulators[M]. New York:Springer, 2012.

[30] Shen S Q, Shan W Y, Lu H Z. Topological Insulator and the Dirac Equation[C]. Spin. World Scientific Publishing Company, 2011, 1(01):33-44.

[31] Sparber C, Markowich P. Semiclassical asymptotics for the Maxwell-Dirac system[J]. Journal of Mathematical Physics, 2003, 44(10):4555-4572.

[32] Strang G. On the construction and comparison of difference schemes[J]. SIAM Journal on Numerical Analysis, 1968, 5(3):506-517.

[33] Thaller B. The Dirac Equation[M]. Springer Science & Business Media, 2013.

[34] Wakano M. Intensely localized solutions of the classical Dirac-Maxwell field equations[J]. Progress of Theoretical Physics, 1966, 35(6):1117-1141.

[35] Zhang Y, Cao L Q, Wong Y S. Multiscale computations for 3d time-dependent Maxwell's equations in composite materials[J]. SIAM Journal on Scientific Computing, 2010, 32(5):2560-2583.

[36] Zhang L, Cao L Q, and Luo J L. Multiscale analysis and computation for a stationary SchrödingerPoisson system in heterogeneous nanostructures[J]. Multiscale Modeling & Simulation, 2014, 12(1):1561-1591.

No related articles found!

--> -->
阅读次数
全文







摘要





Cited

Shared






PDF全文下载地址:

http://www.computmath.com/jssx/CN/article/downloadArticleFile.do?attachType=PDF&id=265
相关话题/数学 计算 工程 科学 北京