Paper Info
Title
Multilevel preconditioning of 2D Rannacher-Turek FE problems: additive and multiplicative methods
Abstract
In the present paper we concentrate on algebraic two-level and multilevel preconditioners for symmetric positive definite problems arising from discretization by Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested (in general). To handle this, a proper two-level basis is required in order to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the methods to the multilevel case. The proposed variants of hierarchical two-level basis are first introduced in a rather general setting. Then, the involved parameters are studied and optimized. As will be shown, the obtained bounds - in particular - give rise to optimal order AMLI methods of additive type. The presented numerical tests fully confirm the theoretical estimates.
Year
DOI
Venue
2006
10.1007/978-3-540-70942-8_6
Numerical Methods and Applications
Keywords
Field
DocType
multilevel case,multiplicative method,general framework,rannacher-turek fe problem,hierarchical two-level basis,algebraic two-level,two-level preconditioners,bilinear finite element,finite element,finite element space,proper two-level basis,general setting,multilevel preconditioning
Applied mathematics,Discrete mathematics,Numerical tests,Discretization,Algebraic number,Multiplicative function,Positive-definite matrix,Finite element method,Quadrilateral,Mathematics,Bilinear interpolation
Conference
Volume
ISSN
Citations 
4310
0302-9743
1
PageRank 
References 
Authors
0.40
5
3
Name
Order
Citations
PageRank
Ivan Georgiev1177.56
Johannes Kraus2162.91
Svetozar Margenov3651161.11