Research Article

Investigation of numerical time-integrations of Maxwell's equations using the staggered grid spatial discretization

  1. I. Faragó1,
  2. R. Horváth2,*,
  3. W. H. A. Schilders3

Article first published online: 4 JAN 2005

DOI: 10.1002/jnm.570

Issue

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

Volume 18, Issue 2, pages 149–169, March/April 2005

Additional Information

How to Cite

Faragó, I., Horváth, R. and Schilders, W. H. A. (2005), Investigation of numerical time-integrations of Maxwell's equations using the staggered grid spatial discretization. Int. J. Numer. Model., 18: 149–169. doi: 10.1002/jnm.570

Author Information

  1. 1

    Eötvös Loránd University Budapest, Pázmány P. sétány 1/C, H-1117 Budapest, Hungary

  2. 2

    University of West Hungary, Erzsébet u. 9, H-9400 Sopron, Hungary

  3. 3

    Philips Research Laboratories Eindhoven, Prof. Holstlaan 4, NL-5656AA, The Netherlands

*University of West Hungary, Erzsébet u. 9, H-9400 Sopron, Hungary

Publication History

  1. Issue published online: 7 FEB 2005
  2. Article first published online: 4 JAN 2005
  3. Manuscript Revised: 1 OCT 2004
  4. Manuscript Accepted: 1 OCT 2004
  5. Manuscript Received: 6 APR 2004

SEARCH

SEARCH BY CITATION

ARTICLE TOOLS

Get PDF (204K)

Keywords:

  • Maxwell's equations;
  • FDTD method;
  • stability;
  • unconditional stability

Abstract

The Yee-method is a simple and elegant way of solving the time-dependent Maxwell's equations. On the other hand, this method has some inherent drawbacks too. The main one is that its stability requires a very strict upper bound for the possible time-steps. This is why, during the last decade, the main goal was to construct such methods that are unconditionally stable. This means that the time-step can be chosen based only on accuracy instead of stability considerations. In this paper we give a uniform treatment of methods that use the same spatial staggered grid approximation as the classical Yee-method. Three other numerical methods are discussed: the Namiki–Zheng–Chen–Zhang alternating direction implicit method (NZCZ), the Kole–Figge-de Raedt method (KFR) and a Krylov-space method. All methods are discussed with non-homogeneous material parameters. We show how the existing finite difference numerical methods are based on the approximation of a matrix exponential. With this formulation we prove the unconditional stability of the NZCZ method without any computer algebraic tool. Moreover, we accelerate the Krylov-space method with a skew-symmetric formulation of the semi-discretized equations. Our main goal is to compare the methods from the point of view of the computational speed. This question is investigated in ID numerical tests. Copyright © 2005 John Wiley & Sons, Ltd.

Get PDF (204K)