@Article{Cheng2016,
author="Cheng, Yingda
and Christlieb, Andrew J.
and Guo, Wei
and Ong, Benjamin",
title="An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics",
journal="Journal of Scientific Computing",
year="2017",
volume="71",
number="3",
pages="959--993",
abstract="In plasma simulations, where the speed of light divided by a
characteristic length is at a much higher frequency
than other relevant parameters in the underlying
system, such as the plasma frequency, implicit
methods begin to play an important role in
generating efficient solutions in these multi-scale
problems. Under conditions of scale separation, one
can rescale Maxwell's equations in such a way as to
give a magneto static limit known as the Darwin
approximation of electromagnetics. In this work, we
present a new approach to solve Maxwell's equations
based on a Method of Lines Transpose (
{\$}{\$}{\backslash}hbox {\{}MOL{\}}^T{\$}{\$} MOL T
) formulation, combined with a fast summation method
with computational complexity
{\$}{\$}O(N{\backslash}log {\{}N{\}}){\$}{\$} O ( N
log N ) , where N is the number of grid points
(particles). Under appropriate scaling, we show that
the proposed schemes result in asymptotic preserving
methods that can recover the Darwin limit of
electrodynamics.",
issn="1573-7691",
doi="10.1007/s10915-016-0328-0",
url="http://dx.doi.org/10.1007/s10915-016-0328-0"
}