Paper Info
Title
Multilevel Preconditioning of Rotated Trilinear Non-conforming Finite Element Problems
Abstract
In this paper algebraic two-level and multilevel preconditioning algorithms for second order elliptic boundary value problems are constructed, where the discretization is done using Rannacher-Turek non-conforming rotated trilinear finite elements. 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 to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method 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. The major contribution of the paper is the derived estimates of the constant 茂戮驴in the strengthened CBS inequality which is shown to allow the efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver.
Year
DOI
Venue
2007
10.1007/978-3-540-78827-0_8
Large-Scale Scientific Computing
Keywords
Field
DocType
related two-level preconditioners,rotated trilinear non-conforming finite,multilevel preconditioning,general framework,hierarchical two-level basis,efficient multilevel extension,two-level preconditioners,finite element,finite element space,proper two-level basis,paper algebraic two-level,general setting,element problems,elliptic boundary value problem
Applied mathematics,Numerical tests,Discretization,Boundary value problem,Mathematical optimization,Algebraic number,Finite element method,Solver,Mathematics
Conference
Volume
ISSN
Citations 
4818
0302-9743
0
PageRank 
References 
Authors
0.34
7
3
Name
Order
Citations
PageRank
Ivan Georgiev1177.56
Johannes Kraus2162.91
Svetozar Margenov3651161.11