Volume 27, Issue 5
Multiscale Computations for the Maxwell–Schrödinger System in Heterogeneous Nanostructures

Chupeng Ma, Jizu Huang, Liqun CaoYanping Lin

Commun. Comput. Phys., 27 (2020), pp. 1443-1469.

Published online: 2020-03

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  • Abstract

In this paper, we study the multiscale computations for the Maxwell– Schrödinger system with rapidly oscillating coefficients under the dipole approximation that describes light-matter interaction in heterogeneous nanostructures. The multiscale asymptotic method and an associated numerical algorithm for the system are presented. We propose an alternating Crank–Nicolson finite element method for solving the homogenized Maxwell–Schödinger system and prove the existence of solutions to the discrete system. Numerical examples are given to validate the efficiency and accuracy of the algorithm.

  • Keywords

Maxwell–Schrödinger system, homogenization, multiscale asymptotic method, Crank–Nicolson scheme.

  • AMS Subject Headings

35Q40, 35Q60, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

machupeng@lsec.cc.ac.cn (Chupeng Ma)

huangjz@lsec.cc.ac.cn (Jizu Huang)

clq@lsec.cc.ac.cn (Liqun Cao)

yanping.lin@polyu.edu.hk (Yanping Lin)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1443, author = {Ma , Chupeng and Huang , Jizu and Cao , Liqun and Lin , Yanping}, title = {Multiscale Computations for the Maxwell–Schrödinger System in Heterogeneous Nanostructures}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {5}, pages = {1443--1469}, abstract = {

In this paper, we study the multiscale computations for the Maxwell– Schrödinger system with rapidly oscillating coefficients under the dipole approximation that describes light-matter interaction in heterogeneous nanostructures. The multiscale asymptotic method and an associated numerical algorithm for the system are presented. We propose an alternating Crank–Nicolson finite element method for solving the homogenized Maxwell–Schödinger system and prove the existence of solutions to the discrete system. Numerical examples are given to validate the efficiency and accuracy of the algorithm.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0004}, url = {http://global-sci.org/intro/article_detail/cicp/15770.html} }
TY - JOUR T1 - Multiscale Computations for the Maxwell–Schrödinger System in Heterogeneous Nanostructures AU - Ma , Chupeng AU - Huang , Jizu AU - Cao , Liqun AU - Lin , Yanping JO - Communications in Computational Physics VL - 5 SP - 1443 EP - 1469 PY - 2020 DA - 2020/03 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0004 UR - https://global-sci.org/intro/article_detail/cicp/15770.html KW - Maxwell–Schrödinger system, homogenization, multiscale asymptotic method, Crank–Nicolson scheme. AB -

In this paper, we study the multiscale computations for the Maxwell– Schrödinger system with rapidly oscillating coefficients under the dipole approximation that describes light-matter interaction in heterogeneous nanostructures. The multiscale asymptotic method and an associated numerical algorithm for the system are presented. We propose an alternating Crank–Nicolson finite element method for solving the homogenized Maxwell–Schödinger system and prove the existence of solutions to the discrete system. Numerical examples are given to validate the efficiency and accuracy of the algorithm.

Chupeng Ma, Jizu Huang, Liqun Cao & Yanping Lin. (2020). Multiscale Computations for the Maxwell–Schrödinger System in Heterogeneous Nanostructures. Communications in Computational Physics. 27 (5). 1443-1469. doi:10.4208/cicp.OA-2019-0004
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