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Semi‐coarsening AMLI algorithms for elasticity problems
Author(s) -
Margenov Svetozar D.
Publication year - 1998
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199809/10)5:5<347::aid-nla137>3.0.co;2-5
Subject(s) - mathematics , poisson distribution , elasticity (physics) , constant (computer programming) , rectangle , algorithm , mathematical optimization , computer science , geometry , statistics , materials science , composite material , programming language
The constant γ in the strengthened Cauchy‐Buniakowski‐Schwarc (CBS) inequality plays a key role in the convergence analysis of the multilevel iterative methods. We consider in this paper the approximation of the two‐dimensional elasticity problem by bilinear rectangle finite elements. Two semi‐coarsening refinement procedures are studied. We prove for both cases new estimates of the constant γ, uniformly on the Poisson ratio. As a result of the presented analysis we obtain an optimal order algebraic multiLevel iteration (AMLI) method for the case of balanced semi‐coarsening mesh refinement. The total computational complexity of the algorithm is proportional to the size of the discrete problem with a proportionality constant independent of the Poisson ratio, that is, the algorithm is of optimal order for almost incompressible elasticity problems. Copyright © 1999 John Wiley & Sons, Ltd.