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Diagonal scaling of stiffness matrices in the Galerkin boundary element method

Ainsworth, Mark; Mclean, B; Tran, T

Description

A boundary integral equation of the first kind is discretised using Galerkin's method with piecewise-constant trial functions. We show how the condition number of the stiffness matrix depends on the number of degrees of freedom and on the global mesh ratio. We also show that diagonal scaling eliminates the latter dependence. Numerical experiments confirm the theory, and demonstrate that in practical computations involving strong local mesh refinement, diagonal scaling dramatically improves the...[Show more]

dc.contributor.authorAinsworth, Mark
dc.contributor.authorMclean, B
dc.contributor.authorTran, T
dc.date.accessioned2015-12-13T23:20:03Z
dc.date.available2015-12-13T23:20:03Z
dc.identifier.issn1446-8735
dc.identifier.urihttp://hdl.handle.net/1885/90538
dc.description.abstractA boundary integral equation of the first kind is discretised using Galerkin's method with piecewise-constant trial functions. We show how the condition number of the stiffness matrix depends on the number of degrees of freedom and on the global mesh ratio. We also show that diagonal scaling eliminates the latter dependence. Numerical experiments confirm the theory, and demonstrate that in practical computations involving strong local mesh refinement, diagonal scaling dramatically improves the conditioning of the Galerkin equations.
dc.publisherAustralian Mathematical Society
dc.sourceANZIAM Journal
dc.titleDiagonal scaling of stiffness matrices in the Galerkin boundary element method
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume42
dc.date.issued2000
local.identifier.absfor010301 - Numerical Analysis
local.identifier.ariespublicationMigratedxPub20922
local.type.statusPublished Version
local.contributor.affiliationAinsworth, Mark, University of New South Wales
local.contributor.affiliationMclean, B, University of New South Wales
local.contributor.affiliationTran, T, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage141
local.bibliographicCitation.lastpage150
dc.date.updated2015-12-12T09:01:46Z
local.identifier.scopusID2-s2.0-33747304581
CollectionsANU Research Publications

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