Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs

doi:10.1007/s10915-019-00936-z

	Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs
	Fang, Zhiwei 1; Li, Jichun 1; Tang, Tao 2; Zhou, Tao3
	2019-07-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	80 期号:1 页码:248-267
摘要	In this paper, we are concerned with the stochastic Galerkin methods for time-dependent Maxwell's equations with random input. The generalized polynomial chaos approach is first adopted to convert the original random Maxwell's equation into a system of deterministic equations for the expansion coefficients (the Galerkin system). It is shown that the stochastic Galerkin approach preserves the energy conservation law. Then, we propose a finite element approach in the physical space to solve the Galerkin system, and error estimates is presented. For the time domain approach, we propose two discrete schemes, namely, the Crank-Nicolson scheme and the leap-frog type scheme. For the Crank-Nicolson scheme, we show the energy preserving property for the fully discrete scheme. While for the classic leap-frog scheme, we present a conditional energy stability property. It is well known that for the stochastic Galerkin approach, the main challenge is how to efficiently solve the coupled Galerkin system. To this end, we design a modified leap-frog type scheme in which one can solve the coupled system in a decouple wayyielding a very efficient numerical approach. Numerical examples are presented to support the theoretical finding.
关键词	Maxwell's equations Finite element method Random inputs Polynomial chaos methods Stochastic Galerkin
DOI	10.1007/s10915-019-00936-z
语种	英语
资助项目	NSF[DMS-1416742] ; NSFC[11671340] ; NSF of China[11822111] ; NSF of China[11688101] ; NSF of China[91630203] ; NSF of China[11571351] ; NSF of China[11731006] ; Science Challenge Project[TZ2018001] ; National Key Basic Research Program[2018YFB0704304] ; NCMIS ; Youth Innovation Promotion Association (CAS)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000468983100009
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34890
专题	计算数学与科学工程计算研究所
通讯作者	Li, Jichun
作者单位	1.Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA 2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Fang, Zhiwei,Li, Jichun,Tang, Tao,et al. Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs[J]. JOURNAL OF SCIENTIFIC COMPUTING,2019,80(1):248-267.
APA	Fang, Zhiwei,Li, Jichun,Tang, Tao,&Zhou, Tao.(2019).Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs.JOURNAL OF SCIENTIFIC COMPUTING,80(1),248-267.
MLA	Fang, Zhiwei,et al."Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs".JOURNAL OF SCIENTIFIC COMPUTING 80.1(2019):248-267.