Volume 29, Issue 1
Analysis and Application of Single Level, Multi-Level Monte Carlo and Quasi-Monte Carlo Finite Element Methods for Time-Dependent Maxwell's Equations with Random Inputs

Xiang Wang, Jichun LiZhiwei Fang

Commun. Comput. Phys., 29 (2021), pp. 211-236.

Published online: 2020-11

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  • Abstract

This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell's equations with uncertain permittivity, permeability and initial conditions. We develop the mathematical analysis of the error estimate for single level Monte Carlo method, multi-level Monte Carlo method, and the quasi-Monte Carlo method. The theoretical results are supplemented by numerical experiments.

  • Keywords

Maxwell's equations, uncertainty quantification, edge element.

  • AMS Subject Headings

65N30, 35L15, 78-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-211, author = {Wang , Xiang and Li , Jichun and Fang , Zhiwei}, title = {Analysis and Application of Single Level, Multi-Level Monte Carlo and Quasi-Monte Carlo Finite Element Methods for Time-Dependent Maxwell's Equations with Random Inputs}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {1}, pages = {211--236}, abstract = {

This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell's equations with uncertain permittivity, permeability and initial conditions. We develop the mathematical analysis of the error estimate for single level Monte Carlo method, multi-level Monte Carlo method, and the quasi-Monte Carlo method. The theoretical results are supplemented by numerical experiments.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0011}, url = {http://global-sci.org/intro/article_detail/cicp/18428.html} }
TY - JOUR T1 - Analysis and Application of Single Level, Multi-Level Monte Carlo and Quasi-Monte Carlo Finite Element Methods for Time-Dependent Maxwell's Equations with Random Inputs AU - Wang , Xiang AU - Li , Jichun AU - Fang , Zhiwei JO - Communications in Computational Physics VL - 1 SP - 211 EP - 236 PY - 2020 DA - 2020/11 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0011 UR - https://global-sci.org/intro/article_detail/cicp/18428.html KW - Maxwell's equations, uncertainty quantification, edge element. AB -

This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell's equations with uncertain permittivity, permeability and initial conditions. We develop the mathematical analysis of the error estimate for single level Monte Carlo method, multi-level Monte Carlo method, and the quasi-Monte Carlo method. The theoretical results are supplemented by numerical experiments.

Xiang Wang, Jichun Li & Zhiwei Fang. (2020). Analysis and Application of Single Level, Multi-Level Monte Carlo and Quasi-Monte Carlo Finite Element Methods for Time-Dependent Maxwell's Equations with Random Inputs. Communications in Computational Physics. 29 (1). 211-236. doi:10.4208/cicp.OA-2020-0011
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