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

Jichun Li & Zhiwei Fang

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

Published online: 2018-09

[An open-access article; the PDF is free to any online user.]

Preview Full PDF 56 1877
Export citation
  • 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

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@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} }
Copy to clipboard
The citation has been copied to your clipboard