### Abstract

We derive a separation of variables solution for time-domain electromagnetic scattering from a perfectly conducting infinite flat plate. The time dependent part of the equations are then used as a model problem in order to study the effects 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. © 2000 Elsevier Science Inc. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 1-26 |

Number of pages | 26 |

Journal | Applied Mathematics and Computation |

Volume | 107 |

Issue number | 1 |

Publication status | Published - Jan 2000 |

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### Keywords

- Electromagnetic scattering
- Numerical analysis
- Retarded potential
- Time-domain

### Cite this

*Applied Mathematics and Computation*,

*107*(1), 1-26.

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*Applied Mathematics and Computation*, vol. 107, no. 1, pp. 1-26.

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

AU - Duncan, Dugald B.

PY - 2000/1

Y1 - 2000/1

N2 - We derive a separation of variables solution for time-domain electromagnetic scattering from a perfectly conducting infinite flat plate. The time dependent part of the equations are then used as a model problem in order to study the effects 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. © 2000 Elsevier Science Inc. All rights reserved.

AB - We derive a separation of variables solution for time-domain electromagnetic scattering from a perfectly conducting infinite flat plate. The time dependent part of the equations are then used as a model problem in order to study the effects 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. © 2000 Elsevier Science Inc. All rights reserved.

KW - Electromagnetic scattering

KW - Numerical analysis

KW - Retarded potential

KW - Time-domain

UR - http://www.scopus.com/inward/record.url?scp=0005326432&partnerID=8YFLogxK

M3 - Article

VL - 107

SP - 1

EP - 26

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 1

ER -