Paper Info
Title
Completeness of generating systems for quadratic splines on adaptively refined criss-cross triangulations.
Abstract
Hierarchical generating systems that are derived from Zwart-Powell (ZP) elements can be used to generate quadratic splines on adaptively refined criss-cross triangulations. We propose two extensions of these hierarchical generating systems, firstly decoupling the hierarchical ZP elements, and secondly enriching the system by including auxiliary functions. These extensions allow us to generate the entire hierarchical spline space - which consists of all piecewise quadratic C 1 -smooth functions on an adaptively refined criss-cross triangulation - if the triangulation fulfills certain technical assumptions. Special attention is dedicated to the characterization of the linear dependencies that are present in the resulting enriched decoupled hierarchical generating system. Hierarchical Zwart-Powell elements are studied.Sufficient conditions for algebraic completeness are given.Construction uses decoupling and partial chessboard functions.Characterization of linear dependencies is provided.
Year
DOI
Venue
2016
10.1016/j.cagd.2016.03.005
Computer Aided Geometric Design
Keywords
Field
DocType
Multilevel spline space,Criss-cross triangulation,Zwart–Powell elements,Completeness
Spline (mathematics),Topology,Mathematical optimization,Algebraic number,Decoupling (cosmology),Quadratic equation,Auxiliary function,Triangulation (social science),Completeness (statistics),Piecewise,Mathematics
Journal
Volume
Issue
ISSN
45
C
0167-8396
Citations 
PageRank 
References 
1
0.36
14
Authors
3
Name
Order
Citations
PageRank
Bert Jüttler1114896.12
Dominik Mokris2182.16
Urška Zore3162.20