Multiscale Computations for the Maxwell-Schrodinger System in Heterogeneous Nanostructures

被引：1

作者：

Ma, Chupeng ^{[1
]}

Huang, Jizu ^{[2
]}

Cao, Liqun ^{[2
]}

Lin, Yanping ^{[1
]}

机构：

[1] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Hong Kong, Peoples R China

[2] Chinese Acad Sci, LSEC, NCMIS,Acad Math & Syst Sci, Univ Chinese Acad Sci,Inst Computat Math & Sci En, Beijing 100190, Peoples R China

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2020年 / 27卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Maxwell-Schrodinger system; homogenization; multiscale asymptotic method; Crank-Nicolson scheme; COUPLED MAXWELL; EQUATIONS; SIMULATION; MODEL;

D O I：

10.4208/cicp.OA-2019-0004

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study the multiscale computations for the Maxwell- Schrodinger 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-Schodinger system and prove the existence of solutions to the discrete system. Numerical examples are given to validate the efficiency and accuracy of the algorithm.

引用

页码：1443 / 1469

页数：27

共 30 条

[1] Simulation of Plasmonics Nanodevices with Coupled Maxwell and Schrodinger Equations using the FDTD Method [J].

Ahmed, Iftikhar ;

Li, Erping .

ADVANCED ELECTROMAGNETICS, 2012, 1 (01) :76-83

[2] A Hybrid Approach for Solving Coupled Maxwell and Schrodinger Equations Arising in the Simulation of Nano-Devices [J].

Ahmed, Iftikhar ;

Khoo, Eng Huat ;

Li, Erping ;

Mittra, Raj .

IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, 2010, 9 :914-917

[3] Homogenization of the Schrodinger equation and effective mass theorems [J].

Allaire, G ;

Piatnitski, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 258 (01) :1-22

[4]

[Anonymous], 1978, ASYMPTOTIC ANAL PERI

[5]

[Anonymous], 2002, Appl. Math., V47, P255

[6] A MULTISCALE METHOD FOR OPTICAL RESPONSES OF NANOSTRUCTURES [J].

Bao, Gang ;

Liu, Di ;

Luo, Songting .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2013, 73 (02) :741-756

[7]

Bossmann L., 2016, THESIS

[8]

Browder F. E., 1965, P S APPL MATH, P24

[9] Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media [J].

Cao, Li-qun ;

Luo, Jian-lan ;

Wang, Chong-yu .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (08) :3955-3973

[10] MULTISCALE ASYMPTOTIC METHOD FOR MAXWELL'S EQUATIONS IN COMPOSITE MATERIALS [J].

Cao, Liqun ;

Zhang, Ya ;

Allegretto, Walter ;

Lin, Yanping .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 47 (06) :4257-4289

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