A new perspective on hierarchical spline spaces for adaptivity

ACTIS, MARCELO; MORIN, PEDRO; PAULETTI, M. SEBASTIÁN

COMPUTERS & MATHEMATICS WITH APPLICATIONS (1987)

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2020 vol. 79 p. 2276 - 2303

0898-1221

We introduce a framework for spline spaces of hierarchical type, based on a parent-children relation, which is very convenient for the analysis as well as the implementation of adaptive isogeometric methods. This framework exploits the innate refinement by functions in the B-splines context, rather than by elements or cells, which is more natural in the finite element context. Furthermore, it entails a new language to handle hierarchical spline spaces, which allows to tackle fundamental questions in a very simple manner. For example, it makes it simple to create hierarchical bases with several desired properties with a refinement procedure which has linear complexity, i.e., the resulting bases have cardinality bounded by the number of initially marked functions.