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

文献类型：期刊论文

作者Fang, Zhiwei2; Li, Jichun2; Tang, Tao3; Zhou, Tao1
刊名JOURNAL OF SCIENTIFIC COMPUTING
出版日期2019-07-01
卷号80期号:1页码:248-267
关键词Maxwell's equations Finite element method Random inputs Polynomial chaos methods Stochastic Galerkin
ISSN号0885-7474
DOI10.1007/s10915-019-00936-z
英文摘要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.
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
语种英语
WOS记录号WOS:000468983100009
出版者SPRINGER/PLENUM PUBLISHERS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/34889]  
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.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
2.Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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