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Two-level additive Schwartz preconditioners for the h-p version of the Galerkin boundary element method for 2-d problems

Tran, T; Stephan, E

Description

We study two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method when used to solve hypersingular integral equations of the first kind, which arise from the Neumann problems for the Laplacian in two dimensions. Overlapping and non-overlapping methods are considered. We prove that the non-overlapping preconditioner yields a system of equations having a condition number bounded by c(1 + logp)2 maxi(1 + logHi/hi) where Hi is the length of the i-th...[Show more]

dc.contributor.authorTran, T
dc.contributor.authorStephan, E
dc.date.accessioned2015-12-10T23:11:19Z
dc.identifier.issn0010-485X
dc.identifier.urihttp://hdl.handle.net/1885/63762
dc.description.abstractWe study two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method when used to solve hypersingular integral equations of the first kind, which arise from the Neumann problems for the Laplacian in two dimensions. Overlapping and non-overlapping methods are considered. We prove that the non-overlapping preconditioner yields a system of equations having a condition number bounded by c(1 + logp)2 maxi(1 + logHi/hi) where Hi is the length of the i-th subdomain, hi is the maximum length of the elements in this subdomain, and p is the maximum polynomial degree used. For the overlapping method, we prove that the condition number is bounded by c(1 + logH/δ)2(1 + logp)2 where δ is the size of the overlap and H = maxiHi. We also discuss the use of the non-overlapping method when the mesh is geometrically graded. The condition number in that case is b ounded by c log2 M, where M is the degrees of freedom.
dc.publisherSpringer
dc.sourceComputing
dc.subjectKeywords: Boundary element method; Galerkin methods; Integral equations; Laplace transforms; Polynomials; Schwarz preconditioners; Matrix algebra Additive Schwarz; Boundary element; Geometric mesh; h-p version Galerkin; Preconditioned conjugate gradient
dc.titleTwo-level additive Schwartz preconditioners for the h-p version of the Galerkin boundary element method for 2-d problems
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume67
dc.date.issued2001
local.identifier.absfor010301 - Numerical Analysis
local.identifier.ariespublicationMigratedxPub845
local.type.statusPublished Version
local.contributor.affiliationTran, T, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationStephan, E, University of Hannover
local.description.embargo2037-12-31
local.bibliographicCitation.startpage57
local.bibliographicCitation.lastpage82
local.identifier.doi10.1007/s006070170016
dc.date.updated2015-12-10T09:21:30Z
local.identifier.scopusID2-s2.0-0034885205
CollectionsANU Research Publications

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