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A new approach to analyticity of Dirichlet-Neumann operators

Published online by Cambridge University Press:  12 July 2007

David P. Nicholls  and
Fernando Reitich
David P. Nicholls
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
Fernando Reitich
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

This paper outlines the theoretical background of a new approach towards an accurate and well-conditioned perturbative calculation of Dirichlet-Neumann operators (DNOs) on domains that are perturbations of simple geometries. Previous work on the analyticity of DNOs has produced formulae that, as we have found, are very ill-conditioned. We show how a simple change of variables can lead to recursions that satisfy analyticity estimates without relying on subtle cancellation properties at the heart of previous formulae.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 6 , December 2001 , pp. 1411 - 1433
Copyright
Copyright © Royal Society of Edinburgh 2001

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