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dc.contributor.authorMadden, Niall
dc.date.accessioned2015-02-06T12:07:39Z
dc.date.available2015-02-06T12:07:39Z
dc.date.issued2012
dc.identifier.otherAMS subject classi cation 65F10
dc.identifier.otherAMS subject classi cation 65N06
dc.identifier.otherAMS subject classi cation 65N22
dc.identifier.otherAMS subject classi cation 65N55
dc.identifier.urihttp://hdl.handle.net/10379/4853
dc.descriptionReporten_US
dc.description.abstractWe consider the problem of solving linear systems of equations that arise in the numerical solution of singularly perturbed ordinary and partial differential equations of reaction-diffusion type. Standard discretization techniques are not suitable for such problems and, so, specially tailored methods are required, usually involving adapted or fitted meshes that resolve important features such as boundary and/or interior layers. In this study, we consider classical finite difference schemes on the layer adapted meshes of Shishkin and Bakhvalov. We show that standard direct solvers exhibit poor scaling behaviour when solving the resulting linear systems. We investigate the use of standard robust multigrid preconditioners for these linear systems, and we propose and prove optimality of a new block-structured preconditioning approach.en_US
dc.description.sponsorshipScience Foundation Ireland - Grant # 08/RFP/CMS1205; Mathematics Initiative 07/MI/007en_US
dc.formatapplication/pdfen_US
dc.language.isoenen_US
dc.subjectMultigriden_US
dc.subjectSingularly perturbeden_US
dc.subjectReaction-diffusionen_US
dc.subjectBoundary-fitted meshesen_US
dc.subjectRobust multigriden_US
dc.subjectPreconditioningen_US
dc.titleRobust solution of singularly perturbed problems using multigrid methods: analysis and results in one and two dimensionsen_US
dc.typeOtheren_US
dc.date.updated2015-02-05T15:59:38Z
dc.local.publishedsourcehttp://www.maths.nuigalway.ie/~niall/Research/MultiGrid_RD_TechReport.pdfen_US
dc.description.peer-reviewednon-peer-reviewed
dc.contributor.funder|~|SFI|~|
dc.internal.rssid8297595
dc.local.contactNiall Madden, School Of Mathematics Statistics, & Applied Mathematics, Room 213, Aras Na Brun, Nui Galway. 3803 Email: niall.madden@nuigalway.ie
dc.local.copyrightcheckedYes
dc.local.versionDRAFT
nui.item.downloads197


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