A simple strategy for defining polynomial spline spaces over hierarchical T-meses

We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision schemes. The proposed technique includes some simple rules for inferring local knot vectors to define -continuous cubic tensor product spline blending functions. Our conjecture is th...

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Detalles Bibliográficos
Autores: Brovka, Marina, López, J. I., Escobar Sánchez, José María, Montenegro Armas, Rafael, Cascón Barbero, José Manuel
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Repositorio:accedaCRIS portal de investigación de la Universidad de las Palmas de Gran Canaria
OAI Identifier:oai:accedacris.ulpgc.es:10553/16442
Acceso en línea:http://hdl.handle.net/10553/16442
Access Level:acceso abierto
Palabra clave:1204 Geometría
1206 Análisis numérico
Isogeometric analysis
Multivariate splines
Local refinement
T-mesh
Nested spaces
Descripción
Sumario:We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision schemes. The proposed technique includes some simple rules for inferring local knot vectors to define -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. 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 mesh. The straightforward implementation of the proposed strategy can make it an attractive tool 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.