A new approach to analyticity of Dirichlet-Neumann operators
David P. Nicholls, Fernando L. Reitich · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2001
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.