@Article{AAMM-1-781,
author = {Lambers , James V.},
title = {A Spectral Time-Domain Method for Computational Electrodynamics},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2009},
volume = {1},
number = {6},
pages = {781--798},
abstract = {<p style="text-align: justify;">Ever since its introduction by Kane Yee over forty years 
ago, the finite-difference time-domain (FDTD) method has been a
widely-used technique for solving the time-dependent Maxwell&#39;s
equations that has also inspired many other methods. This paper
presents an alternative approach to these equations in the case of
spatially-varying electric permittivity and/or magnetic
permeability, based on Krylov subspace spectral (KSS) methods. These
methods have previously been applied to the variable-coefficient
heat equation and wave equation, and have demonstrated high-order
accuracy, as well as stability characteristic of implicit
time-stepping schemes, even though KSS methods are explicit. &nbsp;KSS
methods for scalar equations compute each Fourier coefficient of the
solution using techniques developed by Golub and Meurant for
approximating elements of functions of matrices by Gaussian
quadrature in the spectral, rather than physical, domain. We show
how they can be generalized to coupled systems of equations, such as
Maxwell&#39;s equations, by choosing appropriate basis functions that,
while induced by this coupling, still allow efficient and robust
computation of the Fourier coefficients of each spatial component of
the electric and magnetic fields. &nbsp;We also discuss the application
of block KSS methods to problems involving non-self-adjoint spatial
differential operators, which requires a generalization of the block
Lanczos algorithm of Golub and Underwood to unsymmetric matrices.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.09-m09S02},
url = {http://global-sci.org/intro/article_detail/aamm/8397.html}
}