Incremental unknowns and graph techniques with in-depth refinement

dc.date2007
dc.date.accessioned2012-02-25T04:33:41Z
dc.date.available2012-02-25T04:33:41Z
dc.date.issued2012-02-25
dc.description.abstractWith in-depth refinement, the condition number of the incremental unknowns matrix associated to the Laplace operator is p(d)O(1/ H2)O( logd<sup/>h 3) for the first order incremental unknowns, and q(d)O(1/H2) O((logdh)2) for the second order incremental unknowns, where d is the depth of the refinement, H is the mesh size of the coarsest grid, h is the mesh size of the finest grid, p(d) = d - 1/2 and q(d) = d - 1/2 1/12d(d2 - 1). Furthermore, if block diagonal (scaling) preconditioning is used, the condition number of the preconditioned incremental unknowns matrix associated to the Laplace operator is p(d)O((logdh)2) for the first order incremental unknowns, and q(d)O( logd h ) for the second order incremental unknowns. For comparison, the condition number of the nodal unknowns matrix associated to the Laplace operator is O(1/h2). Therefore, the incremental unknowns preconditioner is efficient with in-depth refinement, but its efficiency deteriorates at some rate as the depth of the refinement grows.es
dc.formatPDFes
dc.identifier.citationInternational Journal of Numerical Analysis and Modeling, Vol.4, Nº2, 149-177, 2007es
dc.identifier.urihttps://hdl.handle.net/10925/734
dc.language.isoenes
dc.sourceInternational Journal of Numerical Analysis and Modelinges
dc.subjectMatemáticases
dc.titleIncremental unknowns and graph techniques with in-depth refinementes
dc.typeArtículo de Revistaes
uct.carreraPlan Común Ingenieríaes
uct.catalogadorFGEes
uct.comunidadIngenieríaes
uct.facultadFacultad de Ingenieríaes
uct.indizacionISIes
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