To main content

Locally Refinable Splines over Box-Partitions

Locally Refinable Splines over Box-Partitions

Category
Report/thesis
Abstract
We address progressive local refinement of splines defined on axes parallel box-partitions and corresponding box-meshes in any space dimension. The refinement is specified by a sequence of mesh-rectangles (axes parallel hyperrectangles) in the mesh defining the spline spaces. In the 2-variate case a mesh-rectangle is a knotline segment. When starting from a tensor-mesh this refinement process builds what we denote an LR-mesh, a special instance of a box-mesh. On the LR-mesh we obtain a collection of hierarchically scaled B-splines, denoted LR B-splines, that forms a nonnegative partition of unity and spans the complete piecewise polynomial space on the mesh when the mesh construction follows certain simple rules. The dimensionality of the spline space can be determined using recent dimension formulas. Oppdragsgiver: SINTEF ; Research Council of Norway
Client
  • SINTEF AS / 90A375
Language
English
Author(s)
Affiliation
  • SINTEF Digital / Mathematics and Cybernetics
  • University of Oslo
Year
2012
Published in
SINTEF Rapport
ISSN
1504-9795
Publisher
SINTEF
Booklet
A22403
ISBN
9788214052824