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ROBUST PRECONDITIONERS FOR LINEAR ELASTICITY FEM ANALYSES
Author(s) -
HLADÍK I.,
REED M. B.,
SWOBODA G.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970615)40:11<2109::aid-nme163>3.0.co;2-1
Subject(s) - preconditioner , conjugate gradient method , finite element method , solver , stiffness matrix , subroutine , mathematical optimization , mathematics , elasticity (physics) , relaxation (psychology) , computer science , factorization , diagonal , algorithm , iterative method , engineering , structural engineering , geometry , psychology , social psychology , materials science , composite material , operating system
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 o is introduced which can make a further significant improvement in performance while maintaining stability. A heuristic for determining a near‐optimal value of o 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.