### Abstract

Language | English |
---|---|

Pages | 1-26 |

Number of pages | 26 |

Journal | Applied Mathematics and Computation |

Volume | 107 |

DOIs | |

Publication status | Published - 2000 |

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### Keywords

- discretisations
- electric field integral equation

### Cite this

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*Applied Mathematics and Computation*, vol. 107, pp. 1-26. https://doi.org/10.1016/S0096-3003(98)10146-7

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the behaviour of time discretisations of the electric field integral equation

AU - Davies, Penny

AU - Duncan, D.B.

PY - 2000

Y1 - 2000

N2 - 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.

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.

KW - discretisations

KW - electric field integral equation

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

U2 - 10.1016/S0096-3003(98)10146-7

DO - 10.1016/S0096-3003(98)10146-7

M3 - Article

VL - 107

SP - 1

EP - 26

JO - Applied Mathematics and Computation

T2 - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -