The multigrid method in solid mechanics. II: Practical applications. (English) Zbl 0724.73270

Parsons, I. D.; Hall, J. F.

Int. J. Numer. Methods Eng. 29, No. 4, 739-753 (1990).

Summary: The performance of the multigrid algorithm is investigated by solving some large, practical, three-dimensional solid mechanics problems. The convergence of the method is sensitive to factors such as the amount of bending present and the degree of mesh non-uniformity, as was also observed in Part I [see the foregoing entry (Zbl 0724.73269)] for two- dimensional problems. However, in contrast to Part I, no proportionality is observed between the total number of operations to convergence and the problem size. Despite such behaviour, the multigrid algorithm proves to be an effective matrix equation solver for solid mechanics problems. It is orders of magnitude faster than a direct factorization method, and yields converged solutions several times faster than the Jacobi preconditioned conjugate gradient method.

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74S05	Finite element methods applied to problems in solid mechanics
65F10	Iterative numerical methods for linear systems

Keywords:

three-dimensional solid mechanics; convergence; matrix equation solver

Citations:

Zbl 0724.73269

References:

[1]	Kanamori, Bull. Seism. Soc. Am. 65 pp 1073– (1975)
[2]	Parsons, Eng. Fract. Mech. 31 pp 45– (1989)
[3]	Parsons, Int. j. numer. methods eng. 29 pp 719– (1990)
[4]	Parsons, Bull. Seism. Soc. Am. 78 pp 931– (1988)