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dc.contributor.authorCiaramella, Gabriele
dc.contributor.authorGander, Martin J.
dc.contributor.authorHalpern, Laurence
dc.contributor.authorSalomon, Julien
dc.date.accessioned2017-10-25T07:34:24Z
dc.date.available2017-10-25T07:34:24Z
dc.date.issued2017-10-18
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1315
dc.descriptionResearch in Pairs 2017en_US
dc.description.abstractThe methods of reflections were invented to obtain approximate solutions of the motion of more than one particle in a given environment, provided that one can represent the solution for one particle rather easily. This motivation is quite similar to the motivation of the Schwarz domain decomposition method, which was invented to prove existence and uniqueness of solutions of the Laplace equation on complicated domains, which are composed of simpler ones, for which existence and uniqueness of solutions was known. Like for Schwarz methods, there is also an alternating and a parallel method of reflections, but interestingly, the parallel method is not always convergent. We carefully trace in this paper the historical development of these methods of reflections, give several precise mathematical formulations, an equivalence result with the alternating Schwarz method for two particles, and also an analysis for a one dimensional model problem with three particles of the alternating, parallel, and a recent averaged parallel method of reflections.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2017,27
dc.subjectAlternating Method of Reflectionsen_US
dc.subjectParallel Method of Reflectionsen_US
dc.subjectAveraged Parallel Method of Reflectionsen_US
dc.subjectAlternating Schwarz Methoden_US
dc.subjectStationary Iterative Methodsen_US
dc.subjectLaplace's Equationen_US
dc.titleReview of the Methods of Reflectionsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2017-27
local.scientificprogramResearch in Pairs 2017en_US
local.series.idOWP-2017-27
local.subject.msc65
local.subject.msc35
dc.identifier.urnurn:nbn:de:101:1-201801093137
dc.identifier.ppn1658648188


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