The stability of numerical approximations of the time domain current induced on thin wire and strip antennas

Penny J. Davies; Dugald B. Duncan; Barbara Zubik-Kowal

doi:10.1016/j.apnum.2004.10.007

The stability of numerical approximations of the time domain current induced on thin wire and strip antennas

Penny J. Davies, Dugald B. Duncan, Barbara Zubik-Kowal

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We derive and analyse collocation approximations of retarded potential integral equations (RPIEs) arising as models of scattering of waves from thin wire and strip antennas. In particular we derive midline collocated and transversely averaged strip RPIEs and show how they are related to the thin wire exact kernel RPIE. We Fourier analyse the temporal stability of spatially exact piecewise constant and linear in time approximations of these three RPIEs. All three are stable when piecewise constant in time approximation is used, but only the transversely averaged strip approximation is stable with piecewise linear time approximation. Numerical results are presented for practical schemes that are piecewise constant or linear in time and space, and these are in close agreement with the predictions of the Fourier analysis. © 2004 IMACS. Published by Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	48-68
Number of pages	21
Journal	Applied Numerical Mathematics
Volume	55
Issue number	1
DOIs	https://doi.org/10.1016/j.apnum.2004.10.007
Publication status	Published - Sept 2005

Keywords

Retarded potential
Stability
Thin strip
Thin wire
Time domain

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10.1016/j.apnum.2004.10.007

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title = "The stability of numerical approximations of the time domain current induced on thin wire and strip antennas",

abstract = "We derive and analyse collocation approximations of retarded potential integral equations (RPIEs) arising as models of scattering of waves from thin wire and strip antennas. In particular we derive midline collocated and transversely averaged strip RPIEs and show how they are related to the thin wire exact kernel RPIE. We Fourier analyse the temporal stability of spatially exact piecewise constant and linear in time approximations of these three RPIEs. All three are stable when piecewise constant in time approximation is used, but only the transversely averaged strip approximation is stable with piecewise linear time approximation. Numerical results are presented for practical schemes that are piecewise constant or linear in time and space, and these are in close agreement with the predictions of the Fourier analysis. {\textcopyright} 2004 IMACS. Published by Elsevier B.V. All rights reserved.",

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author = "Davies, {Penny J.} and Duncan, {Dugald B.} and Barbara Zubik-Kowal",

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T1 - The stability of numerical approximations of the time domain current induced on thin wire and strip antennas

AU - Davies, Penny J.

AU - Duncan, Dugald B.

AU - Zubik-Kowal, Barbara

PY - 2005/9

Y1 - 2005/9

N2 - We derive and analyse collocation approximations of retarded potential integral equations (RPIEs) arising as models of scattering of waves from thin wire and strip antennas. In particular we derive midline collocated and transversely averaged strip RPIEs and show how they are related to the thin wire exact kernel RPIE. We Fourier analyse the temporal stability of spatially exact piecewise constant and linear in time approximations of these three RPIEs. All three are stable when piecewise constant in time approximation is used, but only the transversely averaged strip approximation is stable with piecewise linear time approximation. Numerical results are presented for practical schemes that are piecewise constant or linear in time and space, and these are in close agreement with the predictions of the Fourier analysis. © 2004 IMACS. Published by Elsevier B.V. All rights reserved.

AB - We derive and analyse collocation approximations of retarded potential integral equations (RPIEs) arising as models of scattering of waves from thin wire and strip antennas. In particular we derive midline collocated and transversely averaged strip RPIEs and show how they are related to the thin wire exact kernel RPIE. We Fourier analyse the temporal stability of spatially exact piecewise constant and linear in time approximations of these three RPIEs. All three are stable when piecewise constant in time approximation is used, but only the transversely averaged strip approximation is stable with piecewise linear time approximation. Numerical results are presented for practical schemes that are piecewise constant or linear in time and space, and these are in close agreement with the predictions of the Fourier analysis. © 2004 IMACS. Published by Elsevier B.V. All rights reserved.

KW - Retarded potential

KW - Stability

KW - Thin strip

KW - Thin wire

KW - Time domain

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DO - 10.1016/j.apnum.2004.10.007

M3 - Article

SN - 0168-9274

VL - 55

SP - 48

EP - 68

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 1

ER -

The stability of numerical approximations of the time domain current induced on thin wire and strip antennas

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