AMLI Preconditioning of Pure Displacement Non-conforming Elasticity FEM Systems

Authors:
Tzanio Kolev;Svetozar Margenov
Affiliations:
-;-
Venue:
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Year:
2000

Citing 4
Cited 1

Algebraic multilevel preconditioning methods, II

SIAM Journal on Numerical Analysis
A nonconforming mixed multigrid method for the pure displacement problem in planar linear elasticity

SIAM Journal on Numerical Analysis
Iterative solution methods

Iterative solution methods
On Two Ways of Stabilizing the Hierarchical Basis Multilevel Methods

SIAM Review

Aggregation-based multilevel preconditioning of non-conforming FEM elasticity problems

PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing

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Abstract

This paper is concerned with the pure displacement problem of planar linear elasticity. Our interest is focussed to a locking-free FEM approximation of the problem in the case when the material is almost incompressible. The approximation space is constructed using the Crouzeix-Raviart linear finite elements. Choosing a proper hierarchical basis of this space we define an optimal order algebraic multilevel (AMLI) preconditioner for the related stiffness matrix. Local spectral analysis is applied to find the scaling parameter of the preconditioner as well as to estimate the related constants in the strengthened C.B.S. inequality. A set of numerical tests which illustrate the accuracy of the FEM solution, and the convergence rate of the AMLI PCG method is presented.