Incremental unknowns and graph techniques with in-depth refinement

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datacite.alternateIdentifier.citationINTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,Vol.4,143-177,2007
datacite.creatorGarcia, Salvador
datacite.creatorTone, Florentina
datacite.date2007
datacite.subject.englishfinite differences
datacite.subject.englishincremental unknowns
datacite.subject.englishhierarchical basis
datacite.subject.englishLaplace operator
datacite.subject.englishPoisson equation
datacite.subject.englishChebyshev polynomials
datacite.subject.englishFejer's kernel
datacite.titleIncremental unknowns and graph techniques with in-depth refinement
dc.date.accessioned2021-04-30T16:59:16Z
dc.date.available2021-04-30T16:59:16Z
dc.description.abstractWith in-depth refinement, the condition number of the incremental unknowns matrix associated to the Laplace operator is p(d)O(1/H-2)O(vertical bar logd h vertical bar(3)) for the first order incremental unknowns, and q(d)O(1/H-2)O((logd h)(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) = (d1)/(2) and q(d) = (d-1)/(2) (1)/(12)d(d(2) - 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((log(d) h)(2)) for the first order incremental unknowns, and q(d)O(vertical bar logd(h)vertical bar) for the second order incremental unknowns. For comparison, the condition number of the nodal unknowns matrix associated to the Laplace operator is O(1/h(2)). 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.
dc.identifier.urihttp://repositoriodigital.uct.cl/handle/10925/3786
dc.language.isoen
dc.publisherISCI-INSTITUTE SCIENTIFIC COMPUTING & INFORMATION
dc.sourceINTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
oaire.resourceTypeArticle
uct.catalogadorWOS
uct.indizacionSCI
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