ISSN:
0029-5981
Keywords:
preconditioned conjugate gradients
;
incomplete factorization
;
unstructured irregular grids
;
finite elements
;
linear elasticity
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
This paper deals with two forms of preconditioner which can be easily used with a Conjugate Gradient solver to replace a direct solution subroutine in a traditional engineering finite element package; they are tested in such a package (FINAL) over a range of 2-D and 3-D elasticity problems from geotechnical engineering. Quadratic basis functions are used.A number of modifications to the basic Incomplete Choleski [IC(0)] factorization preconditioner are considered. An algorithm to reduce positive off-diagonal entries is shown in numerical experiments to ensure stability, but at the expense of slow convergence. An alternative algorithm of Jennings and Malik is more successful, and a relaxation parameter ο is introduced which can make a further significant improvement in performance while maintaining stability. A heuristic for determining a near-optimal value of ο is proposed. A second form of preconditioning, symmetrically scaled element by element, due to Bartelt, is also shown to perform robustly over a range of problems; it does not require assembly of the global stiffness matrix, and has great potential for parallelization. © 1997 by John Wiley & Sons, Ltd.
Additional Material:
6 Ill.
Type of Medium:
Electronic Resource
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