Multiscale Computations for the Maxwell–Schrödinger System in Heterogeneous Nanostructures

Authors

  • Chupeng Ma Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.
  • Jizu Huang LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Liqun Cao LSEC, NCMIS, University of Chinese Academy of Sciences, Institute of Computational Mathematicsand Scientific/Engineering Computing,Academyof Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
  • Yanping Lin Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.

DOI:

https://doi.org/10.4208/cicp.OA-2019-0004

Keywords:

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

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.

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Published

2020-05-06

Issue

Vol. 27 No. 5 (2020)

Section

Articles