Analysis and Application of Stochastic Collocation Methods for Maxwell's Equations with Random Inputs
Year: 2018
Author: Jichun Li, Zhiwei Fang
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1305–1326
Abstract
In this paper we develop and analyze the stochastic collocation method for solving the time-dependent Maxwell's equations with random coefficients and subject to random initial conditions. We provide a rigorous regularity analysis of the solution with respect to the random variables. To our best knowledge, this is the first theoretical results derived for the standard Maxwell's equations with random inputs. The rate of convergence is proved depending on the regularity of the solution. Numerical results are presented to confirm the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0101
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1305–1326
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Maxwell's equations random permittivity and permeability stochastic collocation methods uncertainty quantification.
Author Details
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Efficient Stochastic Galerkin Methods for Maxwell’s Equations with Random Inputs
Fang, Zhiwei
Li, Jichun
Tang, Tao
Zhou, Tao
Journal of Scientific Computing, Vol. 80 (2019), Iss. 1 P.248
https://doi.org/10.1007/s10915-019-00936-z [Citations: 5]