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Variational principles in high-frequency scattering*

Published online by Cambridge University Press:  24 October 2008

Ralph D. Kodis
Ralph D. Kodis
Affiliation:
Cavendish Laboratory Cambridge*
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Abstract

A pair of variational principles are formulated for two-dimensional scattering by obstacles. The first of these is in terms of the obstacle boundary values, and it is shown that a simple ‘optical’ trial function leads to an incorrect frequency dependence for the scattering cross-section. In the second, the obstacle is viewed as the analogue of an aperture coupling two half spaces. The geometric optics part of the cross-section can then be made explicit and is split off to leave a stationary form for the frequency correction. The zero-order calculation for the cross-section of a circle, using corresponding ‘optical’ trial functions, is found to have the correct (Ka)−2/3 frequency dependence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 4 , October 1958 , pp. 512 - 529
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

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