Regularity analysis of metamaterial Maxwell's equations with random coefficients and initial conditions

Li Jichun; Fang Zhiwei; Lin Guang

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Regularity analysis of metamaterial Maxwell's equations with random coefficients and initial conditions

机译：具有随机系数和初始条件的超材料麦克斯韦方程组的正则性分析

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摘要

In this paper we develop and analyze the stochastic collocation method for solving the time-dependent metamaterial Maxwell's equations subject to random coefficients and random initial conditions. We provide a rigorous regularity analysis of the solution with respect to the random variables. To our best knowledge, this is the first theoretical results derived for the stochastic metamaterial Maxwell equations. The rate of convergence is proved depending on the regularity of the solution. Numerical results are presented to confirm the theoretical analysis. We also demonstrate that the backward wave propagation phenomenon still exists in random metamaterial. (C) 2018 Elsevier B.V. All rights reserved.

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2018年第15期|24-51|共28页
作者
Li Jichun; Fang Zhiwei; Lin Guang;
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作者单位

Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA;

Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA;

Purdue Univ, Dept Math, W Lafayette, IN 47907 USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Maxwell's equations; Random permittivity and permeability; Stochastic collocation methods; Uncertainty quantification;

机译：麦克斯韦方程;随机介电常数和磁导率;随机配置方法;不确定度量化;

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专利

1. Holder regularity for Maxwell's equations under minimal assumptions on the coefficients [J] . Alberti Giovanni S. Calculus of variations and partial differential equations . 2018,第3期

机译：Maxwell等方程式的持有者规律性在系数上最小的假设下
2. Holder regularity for Maxwell's equations under minimal assumptions on the coefficients [J] . Alberti Giovanni S. Calculus of variations and partial differential equations . 2018,第3期

机译：Maxwell等方程的持有者规律性在系数上最小的假设下
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机译：椭圆律理论是否适用于时间调和各向异性的Maxwell方程，且小于Lipschitz复系数？
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机译：多尺度各向同性随机电导率的准静止麦克斯韦方程的有效系数
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机译：Strichartz估计具有Sobolev正则系数的波动方程。
6. FITTING NONLINEAR ORDINARY DIFFERENTIAL EQUATION MODELS WITH RANDOM EFFECTS AND UNKNOWN INITIAL CONDITIONS USING THE STOCHASTIC APPROXIMATION EXPECTATION–MAXIMIZATION (SAEM) ALGORITHM [O] . Sy- Miin Chow, Zhaohua Lu, Hongtu Zhu, -1

机译：随机逼近-最大化（SAEM）算法拟合具有随机效应和未知初始条件的非线性常微分方程模型
7. Elliptic Regularity Theory Applied to Time Harmonic Anisotropic Maxwell’s Equations with Less than Lipschitz Complex Coefficients [O] . Giovanni S. Alberti, Yves Capdeboscq 2016

机译：椭圆正则性理论在小于Lipschitz复系数的时间调和各向异性maxwell方程中的应用
8. Systems of Linear Algebraic Equations with Random Coefficients and the Numerical Solution of Random Integral Equations [R] . Bharucha-Reid, A. T. 1983

机译：随机系数线性代数方程组及随机积分方程的数值解

Regularity analysis of metamaterial Maxwell's equations with random coefficients and initial conditions

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