Numerical methods for solving the time-dependent Maxwell equations
Abstract
We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to construct a family of unconditionally stable algorithms, the conventional Yee algorithm, and two new variants of the Yee algorithm that do not require the use of the staggered-in-time grid. We also consider a one-step algorithm, based on the Chebyshev polynomial expansion, and compare the computational efficiency of the one-step, the Yee-type, the alternating-direction-implicit, and the unconditionally stable algorithms. For applications where the long-time behavior is of main interest, we find that the one-step algorithm may be orders of magnitude more efficient than present multiple time-step, finite-difference time-domain algorithms.
Cite
@article{arxiv.physics/0210035,
title = {Numerical methods for solving the time-dependent Maxwell equations},
author = {H. De Raedt and J. S. Kole and K. F. L. Michielsen and M. T. Figge},
journal= {arXiv preprint arXiv:physics/0210035},
year = {2007}
}