On the behaviour of time discretisations of the electric field integral equation

Penny Davies, D.B. Duncan

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We derive a separation of variables solution for time-domain electromagnetic scattering from a perfectly conducting in®nite ¯at plate. The time dependent part of the equations are then used as a model problem in order to study the e€ects of various time discretisations on the full scattering problem. We examine and explain how exponential and polynomial instabilities arise in the approximation schemes, and show that the time averaging which is often used in an attempt to stabilise solutions of the full problem acts to destabilise some of the schemes. Our results show that two of the time discretisations can produce good results when coupled with a space-exact approximation, and indicate that they will be useful when coupled with an accurate enough spatial approximation.
LanguageEnglish
Pages1-26
Number of pages26
JournalApplied Mathematics and Computation
Volume107
DOIs
Publication statusPublished - 2000

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Time Discretization
Integral equations
Electric Field
Integral Equations
Electric fields
Scattering
Electromagnetic Scattering
Separation of Variables
Scattering Problems
Approximation
Approximation Scheme
Averaging
Time Domain
Polynomials
Polynomial
Model

Keywords

  • discretisations
  • electric field integral equation

Cite this

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On the behaviour of time discretisations of the electric field integral equation. / Davies, Penny; Duncan, D.B.

In: Applied Mathematics and Computation, Vol. 107, 2000, p. 1-26.

Research output: Contribution to journalArticle

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AU - Davies, Penny

AU - Duncan, D.B.

PY - 2000

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AB - We derive a separation of variables solution for time-domain electromagnetic scattering from a perfectly conducting in®nite ¯at plate. The time dependent part of the equations are then used as a model problem in order to study the e€ects of various time discretisations on the full scattering problem. We examine and explain how exponential and polynomial instabilities arise in the approximation schemes, and show that the time averaging which is often used in an attempt to stabilise solutions of the full problem acts to destabilise some of the schemes. Our results show that two of the time discretisations can produce good results when coupled with a space-exact approximation, and indicate that they will be useful when coupled with an accurate enough spatial approximation.

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UR - http://www.ma.hw.ac.uk/~dugald/research/MAT0135.pdf

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