A STOCHASTIC GALERKIN METHOD FOR MAXWELL EQUATIONS WITH UNCERTAINTY

doi:10.1007/s10473-020-0415-z

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (4): 1091-1104.doi: 10.1007/s10473-020-0415-z

A STOCHASTIC GALERKIN METHOD FOR MAXWELL EQUATIONS WITH UNCERTAINTY

程立正^1,2, 汪波¹, 谢资清¹

1. LCSM(MOE) and School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
2. Information Science and Engineering College, Hunan International Economics University, Changsha 410205, China

收稿日期:2019-03-12 修回日期:2019-09-27 出版日期:2020-08-25 发布日期:2020-08-21
通讯作者: Bo WANG E-mail:bowang@hunnu.edu.cn
作者简介:Lizheng CHENG,E-mail:381880392@qq.com;Ziqing XIE,E-mail:ziqingxie@hunnu.edu.cn
基金资助:
Supported by NSFC (91430107/11771138/ 11171104) and the Construct Program of the Key Discipline in Hunan. The first author was partially supported by Scientific Research Fund of Hunan Provincial Education Department (19B325/19C1059) and Hunan International Economics University (2017A05). The second author was supported by NSFC (11771137), the Construct Program of the Key Discipline in Hunan Province, and a Scientific Research Fund of Hunan Provincial Education Department (16B154).

A STOCHASTIC GALERKIN METHOD FOR MAXWELL EQUATIONS WITH UNCERTAINTY

Lizheng CHENG^1,2, Bo WANG¹, Ziqing XIE¹

1. LCSM(MOE) and School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
2. Information Science and Engineering College, Hunan International Economics University, Changsha 410205, China

Received:2019-03-12 Revised:2019-09-27 Online:2020-08-25 Published:2020-08-21
Contact: Bo WANG E-mail:bowang@hunnu.edu.cn
Supported by:
Supported by NSFC (91430107/11771138/ 11171104) and the Construct Program of the Key Discipline in Hunan. The first author was partially supported by Scientific Research Fund of Hunan Provincial Education Department (19B325/19C1059) and Hunan International Economics University (2017A05). The second author was supported by NSFC (11771137), the Construct Program of the Key Discipline in Hunan Province, and a Scientific Research Fund of Hunan Provincial Education Department (16B154).

摘要/Abstract

摘要： In this article, we investigate a stochastic Galerkin method for the Maxwell equations with random inputs. The generalized Polynomial Chaos (gPC) expansion technique is used to obtain a deterministic system of the gPC expansion coefficients. The regularity of the solution with respect to the random is analyzed. On the basis of the regularity results, the optimal convergence rate of the stochastic Galerkin approach for Maxwell equations with random inputs is proved. Numerical examples are presented to support the theoretical analysis.

关键词: Maxwell equations, random inputs, stochastic Galerkin method, gPC expansion, convergence analysis

Abstract: In this article, we investigate a stochastic Galerkin method for the Maxwell equations with random inputs. The generalized Polynomial Chaos (gPC) expansion technique is used to obtain a deterministic system of the gPC expansion coefficients. The regularity of the solution with respect to the random is analyzed. On the basis of the regularity results, the optimal convergence rate of the stochastic Galerkin approach for Maxwell equations with random inputs is proved. Numerical examples are presented to support the theoretical analysis.

Key words: Maxwell equations, random inputs, stochastic Galerkin method, gPC expansion, convergence analysis

中图分类号:

35Q61

程立正, 汪波, 谢资清. A STOCHASTIC GALERKIN METHOD FOR MAXWELL EQUATIONS WITH UNCERTAINTY[J]. 数学物理学报(英文版), 2020, 40(4): 1091-1104.

Lizheng CHENG, Bo WANG, Ziqing XIE. A STOCHASTIC GALERKIN METHOD FOR MAXWELL EQUATIONS WITH UNCERTAINTY[J]. Acta mathematica scientia,Series B, 2020, 40(4): 1091-1104.

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A STOCHASTIC GALERKIN METHOD FOR MAXWELL EQUATIONS WITH UNCERTAINTY

A STOCHASTIC GALERKIN METHOD FOR MAXWELL EQUATIONS WITH UNCERTAINTY

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