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Efficient solution techniques for a finite element thin plate spline formulation

Stals, Linda

Description

We present a new technique for solving the saddle point problem arising from a finite element based thin plate spline formulation. The solver uses the Sherman–Morrison–Woodbury formula to divide the domain into different regions depending on the properties of the data projection matrix. We analyse the conditioning of the resulting system on certain data distributions and use the results to develop effective preconditioners. We show our approach is efficient for a wide range of parameters by...[Show more]

dc.contributor.authorStals, Linda
dc.date.accessioned2015-07-06T03:27:01Z
dc.date.available2015-07-06T03:27:01Z
dc.identifier.issn0885-7474
dc.identifier.urihttp://hdl.handle.net/1885/14221
dc.description.abstractWe present a new technique for solving the saddle point problem arising from a finite element based thin plate spline formulation. The solver uses the Sherman–Morrison–Woodbury formula to divide the domain into different regions depending on the properties of the data projection matrix. We analyse the conditioning of the resulting system on certain data distributions and use the results to develop effective preconditioners. We show our approach is efficient for a wide range of parameters by testing it on a number of different examples. Numerical results are given in one, two and three dimensions.
dc.publisherSpringer Verlag
dc.rights© Springer Science+Business Media New York 2014
dc.sourceJournal of Scientific Computing
dc.titleEfficient solution techniques for a finite element thin plate spline formulation
dc.typeJournal article
local.identifier.citationvolume63
dcterms.dateAccepted2014-07-21
dc.date.issued2015-05
local.identifier.absfor010301 - Numerical Analysis
local.identifier.ariespublicationa383154xPUB1339
local.publisher.urlhttp://link.springer.com/
local.type.statusPublished Version
local.contributor.affiliationStals, L., Mathematical Sciences Institute, The Australian National University
local.bibliographicCitation.issue2
local.bibliographicCitation.startpage374
local.bibliographicCitation.lastpage409
local.identifier.doi10.1007/s10915-014-9898-x
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2015-12-10T10:35:57Z
local.identifier.scopusID2-s2.0-84926278254
CollectionsANU Research Publications

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