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On the Stability of the Finite-Difference Time-Domain Method

✍ Scribed by Rob F. Remis

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
86 KB
Volume
163
Category
Article
ISSN
0021-9991

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✦ Synopsis

In this paper we give a necessary and sufficient condition for the stability of the finite-difference time-domain method (FDTD method). This is an explicit time stepping method that is used for solving transient electromagnetic field problems. A necessary (but not a sufficient) condition for its stability is usually obtained by requiring that discrete Fourier modes, defined on the FDTD grid, remain bounded as time stepping proceeds. Here we follow a different approach. We rewrite the basic FDTD equations in terms of an iteration matrix and study the eigenvalue problem for this matrix. From the analysis a necessary and sufficient condition for stability of the FDTD method follows. Moreover, we show that for a particular time step the 2-norm of the FDTD iteration matrix is equal to the golden ratio.

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