Volume 10, Issue 6
Analysis and Application of Stochastic Collocation Methods for Maxwell’s Equations with Random Inputs

Jichun Li & Zhiwei Fang

DOI: 10.4208/aamm.OA-2018-0101

Adv. Appl. Math. Mech., 10 (2018), pp. 1305-1326.

Published online: 2018-09

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  • 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.

  • Keywords

Maxwell’s equations random permittivity and permeability stochastic collocation methods uncertainty quantification.

  • AMS Subject Headings

65M10 78A48

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COPYRIGHT: © Global Science Press

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@Article{AAMM-10-1305, author = {}, title = {Analysis and Application of Stochastic Collocation Methods for Maxwell’s Equations with Random Inputs}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0101}, url = {http://global-sci.org/intro/article_detail/aamm/12712.html} }
TY - JOUR T1 - Analysis and Application of Stochastic Collocation Methods for Maxwell’s Equations with Random Inputs JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1305 EP - 1326 PY - 2018 DA - 2018/09 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2018-0101 UR - https://global-sci.org/intro/aamm/12712.html KW - Maxwell’s equations KW - random permittivity and permeability KW - stochastic collocation methods KW - uncertainty quantification. AB -

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.

Jichun Li & Zhiwei Fang. (2020). Analysis and Application of Stochastic Collocation Methods for Maxwell’s Equations with Random Inputs. Advances in Applied Mathematics and Mechanics. 10 (6). 1305-1326. doi:10.4208/aamm.OA-2018-0101
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