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On the relation between FDTD and Fibonacci polynomials

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Title: On the relation between FDTD and Fibonacci polynomials
Authors: Remis, Rob F.1 R.F.Remis@TUDelft.NL
Source: Journal of Computational Physics. Feb2011, Vol. 230 Issue 4, p1382-1386. 5p.
Subjects: Finite differences, Time-domain analysis, Fibonacci sequence, Point mappings (Mathematics), Electromagnetic fields, Chebyshev polynomials
Abstract: Abstract: In this paper we show that the Finite-Difference Time-Domain method (FDTD method) follows the recurrence relation for Fibonacci polynomials. More precisely, we show that FDTD approximates the electromagnetic field by Fibonacci polynomials in Δt A, where Δt is the time step and A is the first-order Maxwell system matrix. By exploiting the connection between Fibonacci polynomials and Chebyshev polynomials of the second kind, we easily obtain the Courant-Friedrichs-Lewy (CFL) stability condition and we show that to match the spectral width of the system matrix, the time step should be chosen as large as possible, that is, as close to the CFL upper bound as possible. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 57072845
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  Data: On the relation between FDTD and Fibonacci polynomials
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Feb2011, Vol. 230 Issue 4, p1382-1386. 5p.
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  Data: <searchLink fieldCode="DE" term="%22Finite+differences%22">Finite differences</searchLink><br /><searchLink fieldCode="DE" term="%22Time-domain+analysis%22">Time-domain analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Fibonacci+sequence%22">Fibonacci sequence</searchLink><br /><searchLink fieldCode="DE" term="%22Point+mappings+%28Mathematics%29%22">Point mappings (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Electromagnetic+fields%22">Electromagnetic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Chebyshev+polynomials%22">Chebyshev polynomials</searchLink>
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  Data: Abstract: In this paper we show that the Finite-Difference Time-Domain method (FDTD method) follows the recurrence relation for Fibonacci polynomials. More precisely, we show that FDTD approximates the electromagnetic field by Fibonacci polynomials in Δt A, where Δt is the time step and A is the first-order Maxwell system matrix. By exploiting the connection between Fibonacci polynomials and Chebyshev polynomials of the second kind, we easily obtain the Courant-Friedrichs-Lewy (CFL) stability condition and we show that to match the spectral width of the system matrix, the time step should be chosen as large as possible, that is, as close to the CFL upper bound as possible. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jcp.2010.11.009
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      – Code: eng
        Text: English
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        PageCount: 5
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      – SubjectFull: Finite differences
        Type: general
      – SubjectFull: Time-domain analysis
        Type: general
      – SubjectFull: Fibonacci sequence
        Type: general
      – SubjectFull: Point mappings (Mathematics)
        Type: general
      – SubjectFull: Electromagnetic fields
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      – SubjectFull: Chebyshev polynomials
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      – TitleFull: On the relation between FDTD and Fibonacci polynomials
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              Text: Feb2011
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