On the method of reflections
Laurent, Philippe; Legendre, Guillaume; Salomon, Julien (2017), On the method of reflections. https://basepub.dauphine.fr/handle/123456789/17127
Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-01439871Date
2017Series title
Cahier de recherche CEREMADE, Université Paris-DauphinePages
24
Metadata
Show full item recordAbstract (EN)
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary, this method is particularly well-suited to numerical solvers relying on integral representation formulas. For the parallel and sequential forms of the method appearing in the literature, we propose a general abstract formulation in a given Hilbert setting and interpret the procedure in terms of subspace corrections. We then prove the unconditional convergence of the sequential form and propose a modification of the parallel one that makes it unconditionally converging. An alternative proof of convergence is provided in a case which does not fit into the previous framework. We finally present some numerical tests.Subjects / Keywords
method of reflectionsRelated items
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