Semi-coarsening AMLI algorithms for elasticity problems
✍ Scribed by Svetozar D. Margenov
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 83 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1070-5325
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✦ Synopsis
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.