Cristin-resultat-ID: 1250242
Sist endret: 19. januar 2016, 00:28
NVI-rapporteringsår: 2015
Resultat
Vitenskapelig oversiktsartikkel/review
2015

On the similarities and differences between Classical Hierarchical, Truncated Hierarchical and LR B-splines

Bidragsytere:
  • Kjetil Andre Johannessen
  • Filippo Remonato og
  • Trond Kvamsdal

Tidsskrift

Computer Methods in Applied Mechanics and Engineering
ISSN 0045-7825
e-ISSN 1879-2138
NVI-nivå 2

Om resultatet

Vitenskapelig oversiktsartikkel/review
Publiseringsår: 2015
Volum: 291
Sider: 64 - 101
Open Access

Importkilder

Scopus-ID: 2-s2.0-84928103929

Klassifisering

Vitenskapsdisipliner

Matematikk og naturvitenskap

Emneord

Adaptive metoder • Splines • Elementmetoder • Geometrisk Modellering for CAD/CAM/CAQ

Beskrivelse Beskrivelse

Tittel

On the similarities and differences between Classical Hierarchical, Truncated Hierarchical and LR B-splines

Sammendrag

Smooth spline functions such as B-splines and NURBS are already an established technology in the field of computer-aided design (CAD) and have in recent years been given a lot of attention from the computer-aided engineering (CAE) community. The advantages of local refinement are obvious for anyone working in either field, and as such, several approaches have been proposed. Among others, we find the three strategies Classical Hierarchical B-splines, Truncated Hierarchical B-splines and Locally Refined B-splines. We will in this paper present these three frameworks and highlight similarities and differences between them. In particular, we will look at the function space they span and the support of the basis functions. We will then analyse the corresponding stiffness and mass matrices in terms of sparsity patterns and conditioning numbers. We show that the basis functions in general do not span the same space, and that conditioning numbers are comparable. Moreover we show that the weighting needed by the Classical Hierarchical basis to maintain partition of unity has significant implications on the conditioning numbers.

Bidragsytere

Kjetil Andre Johannessen

  • Tilknyttet:
    Forfatter
    ved Institutt for matematiske fag ved Norges teknisk-naturvitenskapelige universitet

Filippo Remonato

  • Tilknyttet:
    Forfatter
    ved Institutt for matematiske fag ved Norges teknisk-naturvitenskapelige universitet

Trond Kvamsdal

  • Tilknyttet:
    Forfatter
    ved Institutt for matematiske fag ved Norges teknisk-naturvitenskapelige universitet
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