A preconditioning technique based on element matrix factorizations
Computer Methods in Applied Mechanics and Engineering
An analysis of some element-by-element techniques
Computer Methods in Applied Mechanics and Engineering
On Preconditioning for Finite Element Equations on Irregular Grids
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Programming the Finite Element Method
Programming the Finite Element Method
Efficient generation of large-scale pareto-optimal topologies
Structural and Multidisciplinary Optimization
Stress-constrained topology optimization: a topological level-set approach
Structural and Multidisciplinary Optimization
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Finite element analysis of problems in structural and geotechnical engineering results in linear systems where the unknowns are displacements 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 advantageous 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 components. This new method appears to offer a significant improvement in performance.