dc.contributor.author Pettersen, Kjell Fredrik dc.date.accessioned 2017-02-28T10:54:42Z dc.date.available 2017-02-28T10:54:42Z dc.date.created 2015-09-24T18:12:30Z dc.date.issued 2013 dc.identifier.isbn 9788214053135 dc.identifier.uri http://hdl.handle.net/11250/2432305 dc.description.abstract In this paper, we define the topological structures for an arbitrary axis-aligned box partition of a parametric d-dimensional box-shaped limited domain in R^d. Then we define the d-variate spline space over this partition with given polynomial degrees and arbitrary continuity constraints. We then use homological techniques to show that the dimension of this spline space can be split up as dim S(N) = C + H, where the first term is a combinatorial easily calculated term that only depends on the topological structure, polynomial degrees and continuity constraints, while the second term is an alternating sum of dimensions of homological terms. They are often zero, but not always, and might even in some special situations depend on the parameterization.   We give explicit expressions for the terms in tensor product spaces, before we look at how the homology modules are tied together during a refinement process. Eventually we discuss the cases d=2 and d=3. Oppdragsgiver: SINTEF dc.language.iso eng nb_NO dc.publisher SINTEF nb_NO dc.relation.ispartof SINTEF Rapport dc.relation.ispartofseries SINTEF Rapport; dc.title On the dimension of multivariate spline spaces nb_NO dc.type Research report nb_NO dc.source.pagenumber 57 nb_NO dc.source.issue A23875 nb_NO dc.identifier.cristin 1268610 dc.relation.project Stiftelsen SINTEF: 90511201 nb_NO cristin.unitcode 7401,90,11,0 cristin.unitname Anvendt matematikk cristin.ispublished true cristin.fulltext original
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