Heriot-Watt Mathematics Report Series
HWM97-40, 5 December 1997
On the behaviour of time discretisations of the electric field integral equation
P J Davies and D B Duncan
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.
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