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Powell–Sabin spline based multilevel preconditioners for the biharmonic equation
- Source :
-
Applied Numerical Mathematics . May2010, Vol. 60 Issue 5, p527-530. 4p. - Publication Year :
- 2010
-
Abstract
- Abstract: The Powell–Sabin (PS) piecewise quadratic finite element on the PS 12-split of a triangulation is a common choice for the construction of a BPX-type preconditioner for the biharmonic equation. In this note we investigate the related Powell–Sabin element on the PS 6-split instead of the PS 12-split for the construction of such preconditioners. For the PS 6-split element multilevel spaces can be created using a -refinement scheme instead of the traditional dyadic scheme. Topologically -refinement has many advantages: it is a slower refinement than the dyadic split operation, and it alternates the orientation of the refined triangles. Therefore we expect a reduction of the amount of work when compared to the PS 12-split element BPX preconditioner, although both methods have the same asymptotical complexity. Numerical experiments confirm this statement. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 60
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 50226775
- Full Text :
- https://doi.org/10.1016/j.apnum.2010.01.002