@Article{IJNAM-15-6,
author = {Vrushali, Bokil, A. and Sakkaplangkul, Puttha},
title = {Construction and Analysis of Weighted Sequential Splitting FDTD Methods for the 3D Maxwell's Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2018},
volume = {15},
number = {6},
pages = {747--784},
abstract = {<p style="text-align: justify;">In this paper, we present a one parameter family of fully discrete Weighted Sequential
Splitting (WSS)-finite difference time-domain (FDTD) methods for Maxwell’s equations in three
dimensions. In one time step, the Maxwell WSS-FDTD schemes consist of two substages each
involving the solution of several 1D discrete Maxwell systems. At the end of a time step we take
a weighted average of solutions of the substages with a weight parameter $θ$, $0 ≤ θ ≤ 1$. Similar
to the Yee-FDTD method, the Maxwell WSS-FDTD schemes stagger the electric and magnetic
fields in space in the discrete mesh. However, the Crank-Nicolson method is used for the time
discretization of all 1D Maxwell systems in our splitting schemes. We prove that for all values of $θ$,
the Maxwell WSS-FDTD schemes are unconditionally stable, and the order of accuracy is of first
order in time when $θ\neq 0.5$, and of second order when $θ = 0.5$. The Maxwell WSS-FDTD schemes
are of second order accuracy in space for all values of $θ$. We prove the convergence of the Maxwell
WSS-FDTD methods for all values of the weight parameter $θ$ and provide error estimates. We
also analyze the discrete divergence of solutions to the Maxwell WSS-FDTD schemes for all values
of $θ$ and prove that for $θ\neq 0.5$ the discrete divergence of electric and magnetic field solutions is
approximated to first order, while for $θ = 0.5$ we obtain a third order approximation to the exact
divergence. Numerical experiments and examples are given that illustrate our theoretical results.</p>},
issn = {2617-8710},
doi = {https://doi.org/2018-IJNAM-12608},
url = {https://global-sci.com/article/83148/construction-and-analysis-of-weighted-sequential-splitting-fdtd-methods-for-the-3d-maxwells-equations}
}