A new perspective on hierarchical spline spaces for adaptivity
| Autor: | M. Sebastian Pauletti, Marcelo Actis, Pedro Morin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Linear complexity
Theoretical computer science Exploit 010103 numerical & computational mathematics Numerical Analysis (math.NA) 01 natural sciences Finite element method 010101 applied mathematics Constructed language Computational Mathematics Spline (mathematics) Computational Theory and Mathematics Modeling and Simulation Bounded function FOS: Mathematics 65D07 65Y99 Mathematics - Numerical Analysis 0101 mathematics Mathematics |
| Popis: | 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. Such framework makes it simple to create hierarchical \emph{basis} with \emph{control on the overlapping}. Linear independence is always desired for the well posedness of the linear systems, and to avoid redundancy. The control on the overlapping of basis functions from different levels is necessary to close theoretical arguments in the proofs of optimality of adaptive methods. In order to guarantee linear independence, and to control the overlapping of the basis functions, some basis functions additional to those initially marked must be refined. However, with our framework and refinement procedures, the complexity of the resulting bases is under control, i.e., the resulting bases have cardinality bounded by the number of initially marked functions. |
| Databáze: | OpenAIRE |
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