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Construction of polynomial spline spaces over quadtree and octree T-meshes

Brovka, M. and J.I. Lopez, J.M. Escobar, J.M. Cascon, R. Montenegro

23rd International Meshing Roundtable, Elsevier Ltd., October 12-15 2014


23rd International Meshing Roundtable
London, UK
October 12-15,2014

University Institute for Intelligent Systems and Numerical Applications in Engineering, SIANI, University of Las Palmas de Gran Canaria, Spain
Department of Economics and History of Economics, Faculty of Economics and Management, University of Salamanca, Spain

We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. The straightforward implementation of the proposed strategy and the simplicity of tree structures can make it attractive for its use in geometric design and isogeometric analysis. In this paper we give a detailed description of our technique and illustrate some examples of its application in isogeometric analysis performing adaptive refinement for 2D and 3D problems.

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