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A STOCHASTIC GALERKIN METHOD FOR MAXWELL EQUATIONS WITH UNCERTAINTY

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【作者】 程立正； 汪波； 谢资清；

【Author】 Lizheng CHENG;Bo WANG;Ziqing XIE;LCSM (MOE) and School of Mathematics and Statistics,Hunan Normal University;Information Science and Engineering College,Hunan International Economics University;

【通讯作者】 汪波;

【机构】 LCSM (MOE) and School of Mathematics and Statistics,Hunan Normal University； Information Science and Engineering College,Hunan International Economics University；

【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.

【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.

【关键词】 Maxwell equations； random inputs； stochastic Galerkin method； gPC expansion； convergence analysis；
【Key words】 Maxwell equations； random inputs； stochastic Galerkin method； gPC expansion； convergence analysis；
【基金】 Supported by NSFC (91430107/11771138/11171104);the Construct Program of the Key Discipline in Hunan;partially supported by Scientific Research Fund of Hunan Provincial Education Department (19B325/19C1059);Hunan International Economics University (2017A05);supported by NSFC (11771137);the Construct Program of the Key Discipline in Hunan Province;a Scientific Research Fund of Hunan Provincial Education Department (16B154)
  • 【文献出处】 Acta Mathematica Scientia ,数学物理学报(英文版) , 编辑部邮箱 ,2020年04期
  • 【分类号】O441
  • 【下载频次】18
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