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Volume 12, Issue 3
Convergence Analysis of Stochastic Collocation Methods for Maxwell Equations with Random Inputs

Lizheng Cheng, Jiaju Man & Ziqing Xie

DOI: 10.4208/nmtma.OA-2018-0023

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 824-844.

Published online: 2019-04

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  • Abstract

In this paper, we consider a stochastic collocation method for the Maxwell equations with random inputs. We first verify the regularity of the solutions for the model problem, which depends on the random dielectric constant, random magnetic permeability and the initial and boundary data. Then the convergence of our numerical approach is proved. Further some numerical examples are presented to support the analysis.

  • Keywords

Maxwell equations, convergence analysis, stochastic collocation methods, Lagrange interpolation, regularity.

  • AMS Subject Headings

35Q61, 65C30, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-12-824, author = {Lizheng Cheng, Jiaju Man and Ziqing Xie}, title = {Convergence Analysis of Stochastic Collocation Methods for Maxwell Equations with Random Inputs}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {3}, pages = {824--844}, abstract = {

In this paper, we consider a stochastic collocation method for the Maxwell equations with random inputs. We first verify the regularity of the solutions for the model problem, which depends on the random dielectric constant, random magnetic permeability and the initial and boundary data. Then the convergence of our numerical approach is proved. Further some numerical examples are presented to support the analysis.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0023}, url = {http://global-sci.org/intro/article_detail/nmtma/13132.html} }
TY - JOUR T1 - Convergence Analysis of Stochastic Collocation Methods for Maxwell Equations with Random Inputs AU - Lizheng Cheng, Jiaju Man & Ziqing Xie JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 824 EP - 844 PY - 2019 DA - 2019/04 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0023 UR - https://global-sci.org/intro/article_detail/nmtma/13132.html KW - Maxwell equations, convergence analysis, stochastic collocation methods, Lagrange interpolation, regularity. AB -

In this paper, we consider a stochastic collocation method for the Maxwell equations with random inputs. We first verify the regularity of the solutions for the model problem, which depends on the random dielectric constant, random magnetic permeability and the initial and boundary data. Then the convergence of our numerical approach is proved. Further some numerical examples are presented to support the analysis.

Lizheng Cheng, Jiaju Man and Ziqing Xie. (2019). Convergence Analysis of Stochastic Collocation Methods for Maxwell Equations with Random Inputs. Numerical Mathematics: Theory, Methods and Applications. 12 (3). 824-844. doi:10.4208/nmtma.OA-2018-0023
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