TY - JOUR
T1 - Analysis and Application of Stochastic Collocation Methods for Maxwell's Equations with Random Inputs
AU - Li , Jichun
AU - Fang , Zhiwei
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1305
EP - 1326
PY - 2018
DA - 2018/09
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2018-0101
UR - https://global-sci.org/intro/article_detail/aamm/12712.html
KW - Maxwell's equations, random permittivity and permeability, stochastic collocation
methods, uncertainty quantification.
AB - <p style="text-align: justify;">In this paper we develop and analyze the stochastic collocation method for
solving the time-dependent Maxwell&#39;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&#39;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.</p>