Cristin-resultat-ID: 1268610
Sist endret: 24. februar 2017, 11:56
Resultat
Rapport
2013

On the dimension of multivariate spline spaces

Bidragsytere:
  • Kjell Fredrik Pettersen

Utgiver/serie

Utgiver

SINTEF

Serie

SINTEF Rapport
ISSN 1504-9795

Om resultatet

Rapport
Publiseringsår: 2013
Hefte: A23875
Antall sider: 57
ISBN: 9788214053135
Open Access

Importkilder

SINTEF AS-ID: A23875

Beskrivelse Beskrivelse

Tittel

On the dimension of multivariate spline spaces

Sammendrag

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

Bidragsytere

Kjell Fredrik Pettersen

  • Tilknyttet:
    Forfatter
    ved Mathematics and Cybernetics ved SINTEF AS
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