A new approach to analyticity of Dirichlet-Neumann operators
- 1 October 2001
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 131 (6) , 1411-1433
- https://doi.org/10.1017/s0308210500001463
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.Keywords
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