Journal
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
Volume 10, Issue 6, Pages 1305-1326Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/aamm.OA-2018-0101
Keywords
Maxwell's equations; random permittivity and permeability; stochastic collocation methods; uncertainty quantification
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Funding
- National Natural Science Foundation of China (NSFC) [11671340]
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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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