A general stability analysis of FIT/FDTD applied to lossy dielectrics and lumped elements: Research Articles

  • Authors:

  • F. Edelvik;R. Schuhmann;T. Weiland

  • Affiliations:

  • Technische Universität Darmstadt, Institut für Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstr. 8, D-64289 Darmstadt, Germany;Technische Universität Darmstadt, Institut für Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstr. 8, D-64289 Darmstadt, Germany;Technische Universität Darmstadt, Institut für Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstr. 8, D-64289 Darmstadt, Germany

  • Venue:
  • International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
  • Year:
  • 2004

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Abstract

Stability analysis of the finite-difference time-domain (FDTD) method is usually performed using von Neumann analysis, where a necessary condition for stability is obtained by requiring the amplitude of discrete Fourier modes defined on the grid to remain bounded. However, this limits the analysis to homogeneous materials, equidistant grids and unbounded domains. A rare situation in practical computations. In this paper we analytically derive sufficient conditions for stability of FDTD using the energy method. This method does not have the restrictions of von Neumann analysis and we are therefore able to derive closed-form conditions for stability in the case of non-homogeneous and lossy dielectrics, non-homogeneous permeability and varying cell sizes. Moreover, the analysis is applied to different lumped elements. In addition, a discussion of advantages and disadvantages of different discrete energy definitions in FDTD is included. Copyright © 2004 John Wiley & Sons, Ltd.