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

Fang, Zhiwei1; Li, Jichun1; Tang, Tao2; Zhou, Tao3

2019-07

10.1007/s10915-019-00936-z

JOURNAL OF SCIENTIFIC COMPUTING   影响因子和分区

0885-7474

1573-7691

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.

Maxwell's equations Finite element method Random inputs Polynomial chaos methods Stochastic Galerkin

SCI ; EI

英语

其他

National Key Basic Research Program[2018YFB0704304]

Mathematics

Mathematics, Applied

WOS:000468983100009

SPRINGER/PLENUM PUBLISHERS

20191106619058

Galerkin methods ; Maxwell equations ; Stability ; Stochastic systems ; Time domain analysis

Mathematics:921 ; Systems Science:961

MATHEMATICS

Web of Science

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

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.

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.

Fang, Zhiwei,et al."Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs".JOURNAL OF SCIENTIFIC COMPUTING 80.1(2019):248-267.