Multiscale computations for the maxwell-schrödinger system in heterogeneous nanostructures

Chupeng Ma; Jizhou Huang; Liqun Cao; Yanping Lin

doi:10.4208/CICP.OA-2019-0004

Multiscale computations for the maxwell-schrödinger system in heterogeneous nanostructures

Chupeng Ma, Jizhou Huang, Liqun Cao, Yanping Lin

Department of Applied Mathematics

Research output: Journal article publication › Journal article › Academic research › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	1443-1469
Number of pages	27
Journal	Communications in Computational Physics
Volume	27
Issue number	5
DOIs	https://doi.org/10.4208/CICP.OA-2019-0004
Publication status	Published - May 2020

Keywords

Crank-Nicolson scheme
Homogenization
Maxwell-Schrödinger system
Multiscale asymptotic method

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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10.4208/CICP.OA-2019-0004

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title = "Multiscale computations for the maxwell-schr{\"o}dinger system in heterogeneous nanostructures",

abstract = "In this paper, we study the multiscale computations for the Maxwell-Schr{\"o}dinger 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-Sch{\"o}dinger 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 = "Crank-Nicolson scheme, Homogenization, Maxwell-Schr{\"o}dinger system, Multiscale asymptotic method",

author = "Chupeng Ma and Jizhou Huang and Liqun Cao and Yanping Lin",

note = "Funding Information: The work of L.Q. Cao is supported by National Natural Science Foundation of China (grants 11971030, 11571353, 91330202). Publisher Copyright: {\textcopyright} 2020 Global-Science Press",

year = "2020",

month = may,

doi = "10.4208/CICP.OA-2019-0004",

language = "English",

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T1 - Multiscale computations for the maxwell-schrödinger system in heterogeneous nanostructures

AU - Ma, Chupeng

AU - Huang, Jizhou

AU - Cao, Liqun

AU - Lin, Yanping

PY - 2020/5

Y1 - 2020/5

N2 - 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.

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.

KW - Crank-Nicolson scheme

KW - Homogenization

KW - Maxwell-Schrödinger system

KW - Multiscale asymptotic method

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U2 - 10.4208/CICP.OA-2019-0004

DO - 10.4208/CICP.OA-2019-0004

M3 - Journal article

SN - 1815-2406

VL - 27

SP - 1443

EP - 1469

JO - Communications in Computational Physics

JF - Communications in Computational Physics

IS - 5

ER -

Multiscale computations for the maxwell-schrödinger system in heterogeneous nanostructures

Abstract

Keywords

ASJC Scopus subject areas

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