TY - JOUR
T1 - Maxwell Solutions in Media with Multiple Random Interfaces
AU - Jung , C.-Y.
AU - Kwon , B.
AU - Mahalov , A.
AU - Nguyen , T. B.
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 193
EP - 212
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/521.html
KW - Maxwell Equations, Evolution of probability distribution, Monte Carlo simulation, Stochastic partial differential equation, random media, random interface, Polynomial chaos.
AB - <p style="text-align: justify; margin-bottom: 10px;">A hybrid operator splitting method is developed for computations of two-dimensional transverse magnetic Maxwell equations in media with multiple random interfaces. By projecting
the solutions into the random space using the polynomial chaos (PC) projection method, the
deterministic and random parts of the solutions are solved separately.<br/>There are two independent stages in the algorithm: the Yee scheme with domain decomposition
implemented on a staggered grid for the deterministic part and the Monte Carlo sampling in the
post-processing stage. These two stages of the algorithm are subject of computational studies.
A parallel implementation is proposed for which the computational cost grows linearly with the
number of random interfaces. Output statistics of Maxwell solutions are obtained including means,
variance and time evolution of cumulative distribution functions (CDF). The computational results
are presented for several configurations of domains with random interfaces.<br/>The novelty of this article lies in using level set functions to characterize the random interfaces
and, under reasonable assumptions on the random interfaces (see Figure 1), the dimensionality
issue from the PC expansions is resolved (see Sections 1.1.2 and 1.2).</p>