Title

Analysis and Application of Stochastic Collocation Methods for Maxwell’s Equations with Random Inputs

Document Type

Article

Publication Date

9-1-2018

Publication Title

Advances in Applied Mathematics and Mechanics

Volume

10

Issue

6

First page number:

1305

Last page number:

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.

Keywords

Maxwell's equations; random permittivity and permeability; stochastic collocation methods; uncertainty quantification

Disciplines

Applied Mathematics

Language

English

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