dc.contributor.author Paszynski, M. dc.contributor.author Pardo, D. dc.contributor.author Calo, V.M. dc.date.accessioned 2016-06-13T13:11:52Z dc.date.available 2016-06-13T13:11:52Z dc.date.issued 2015-12-31 dc.identifier.issn 0898-1221 dc.identifier.uri http://hdl.handle.net/20.500.11824/101 dc.description.abstract We analyse the performance of direct solvers when applied to a system of linear equations arising from an $h$-adapted, $C^0$ finite element space. Theoretical estimates are derived for typical $h$-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of $h$-adaptive grids significantly reduces the cost of the direct solver algorithm $per$ $unknown$ as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver $per$ $unknown$ is lower when employing anisotropic refinements as opposed to isotropic ones. dc.format application/pdf dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Direct solver dc.subject Finite element method dc.subject $h$-version refinement dc.subject Singularities dc.title Direct solvers performance on h-adapted grids en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1016/j.camwa.2015.05.007 dc.relation.publisherversion http://www.sciencedirect.com/science/article/pii/S0898122115002187 dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Computers and Mathematics with Applications en_US
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