TITLE

Semi-coarsening AMLI preconditioning of higher order elliptic problems

AUTHOR(S)
Kraus, J.; Lymbery, M.; Margenov, S.
PUB. DATE
October 2012
SOURCE
AIP Conference Proceedings;Oct2012, Vol. 1487 Issue 1, p30
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The present paper presents the construction of a robust multilevel preconditioner for anisotropic bicubic finite element (FE) elliptic problems. More precisely, the behavior of the constant in the strengthened CBS inequality, which is important for studying (approximate) block factorizations of FE stiffness matrices, is analyzed in the case when the underlying conforming FE space consists of piecewise bicubic functions, and is decomposed according to hierarchical splittings that are based on semi-coarsening of the FE mesh. The presented theoretical estimates are further confirmed by numerically computed CBS constants for a rich set of parameters (coarsening factor and anisotropy ratio). The problem of solving efficiently systems with the pivot block matrices arising in the hierarchical basis two-level matrices is also addressed in this paper. Finally, combining the proven uniform estimates with the theory of the Algebraic Multilevel Iteration (AMLI) methods an optimal order multilevel algorithm whose total computational cost is proportional to the size of the discrete problem with a proportionality constant independent of the anisotropy ratio is obtained.
ACCESSION #
82145849

 

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