Incremental unknowns and graph techniques with in-depth refinement

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dc.contributor.authorGarcia, Salvador
dc.contributor.authorTone, Florentina
dc.date2007
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.citationINTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,Vol.4,143-177,2007
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
dc.subject.englishfinite differences
dc.subject.englishincremental unknowns
dc.subject.englishhierarchical basis
dc.subject.englishLaplace operator
dc.subject.englishPoisson equation
dc.subject.englishChebyshev polynomials
dc.subject.englishFejer's kernel
dc.titleIncremental unknowns and graph techniques with in-depth refinement
dc.typeArticle
uct.catalogadorWOS
uct.indizacionSCI
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