Summary: An element-based displacement preconditioner for linear
C.E. Augarde a,*, A. Ramage b
, J. Staudacher a
School of Engineering, Durham University, South Road, Durham DH1 3LE, UK
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK
Received 20 March 2006; accepted 6 August 2006
Finite element analysis of problems in structural and geotechnical engineering results in linear systems where the unknowns are dis-
placements and rotations at nodes. Although the solution of these systems can be carried out using either direct or iterative methods, in
practice the matrices involved are usually very large and sparse (particularly for 3D problems) so an iterative approach is often advan-
tageous in terms of both computational time and memory requirements. This memory saving can be further enhanced if the method used
does not require assembly of the full coefficient matrix during the solution procedure. One disadvantage of iterative methods is the need
to apply preconditioning to improve convergence. In this paper, we review a range of established element-based preconditioning methods
for linear elastic problems and compare their performance with a new method based on preconditioning with element displacement com-
ponents. This new method appears to offer a significant improvement in performance.
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Keywords: Finite elements; Iterative solvers; Preconditioning; Elasticity; Geotechnics; Structures