The FDTD method and its relation to Fibonacci polynomials

Author

Remis, R.F.

Author_Institution

Circuits & Syst. Group, Delft Univ. of Technol., Delft, Netherlands

fYear

2011

fDate

12-16 Sept. 2011

Firstpage

271

Lastpage

274

Abstract

In this paper we show that the Finite-Difference Time-Domain method (FDTD method) follows the recurrence relation for Fibonacci polynomials. This observation allows us to easily derive the Courant-Friedrichs-Lewy stability condition by exploiting the connection between Fibonacci polynomials and Chebyshev polynomials of the second kind. In addition, we compare FDTD with the Spectral Lanczos Decomposition method (SLDM) and show that to capture the evolution of the fields in time, SLDM adjust itself to the spectrum of the system matrix, while FDTD takes only extremal eigenvalue information into account.

Keywords

Fibonacci sequences; computational electromagnetics; eigenvalues and eigenfunctions; finite difference time-domain analysis; polynomials; Chebyshev polynomials; Courant-Friedrichs-Lewy stability condition; Fibonacci polynomials; computational electromagnetics; eigenvalue information; finite difference time-domain analysis; recurrence relation; spectral Lanczos decomposition method; Chebyshev approximation; Finite difference methods; Magnetic domains; Polynomials; Time domain analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Electromagnetics in Advanced Applications (ICEAA), 2011 International Conference on

Conference_Location

Torino

Print_ISBN

978-1-61284-976-8

Type

conf

DOI

10.1109/ICEAA.2011.6046303

Filename

6046303