ROBUST PRECONDITIONERS FOR LINEAR ELASTICITY FEM ANALYSES

✍ Scribed by I. HLADÍK; M. B. REED; G. SWOBODA

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 210 KB
• Volume: 40
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19970615)40:11<2109::aid-nme163>3.0.co;2-1

✦ Synopsis

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 ÿnite 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 modiÿcations to the basic Incomplete Choleski [IC(0)] factorization preconditioner are considered. An algorithm to reduce positive o -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 ! is introduced which can make a further signiÿcant improvement in performance while maintaining stability. A heuristic for determining a near-optimal value of ! 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 sti ness matrix, and has great potential for parallelization.