Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems

Journal Article · Wed Jul 01 04:00:00 EDT 1992 · SIAM Journal on Matrix Analysis and Applications

DOI:https://doi.org/10.1137/0613057· OSTI ID:7152633

D'Azevedo, E. F.; Forsyth, P. A.; Tang, W. P. ^[1]

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1. Univ. of Waterloo, Ontario (Canada)

It is well known that the ordering of the unknowns can have a significant effect on the convergence of preconditioned conjugate gradient (PCG) methods. There has been considerable experimental work on the effects of ordering for finite difference problems. In many cases, good results have been obtained with preconditioners based on diagonal, spiral, red/black reduced system orderings, or some others. The reduced system approach generally gives rapid convergence. There has been comparatively less work on the effect of ordering for finite element problems on unstructured meshes. In this paper, an ordering technique for unstructured grid problems is developed. At any stage of the partial elimination, the next pivot node is selected so as to minimize the norm of the discarded fill matrix. Numerical results are given for model problems and for problems arising in groundwater contamination. Computations are reported for two-dimensional triangular grids, and for three-dimensional tetrahedral grids. The examples show that ordering is important even if a reduced system (based on a generalized red/black ordering) method is used.

• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 7152633
• Journal Information: SIAM Journal on Matrix Analysis and Applications, Journal Name: SIAM Journal on Matrix Analysis and Applications Journal Issue: 3 Vol. 13; ISSN SJMAEL; ISSN 0895-4798
• Publisher: SIAM
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
540200 -- Environment
Terrestrial-- (1990-)
97 MATHEMATICS AND COMPUTING
990200* -- Mathematics & Computers
CALCULATION METHODS
CONTAMINATION
CONVERGENCE
FACTORIZATION
FINITE DIFFERENCE METHOD
GROUND WATER
HYDROGEN COMPOUNDS
ITERATIVE METHODS
MATHEMATICAL MODELS
MESH GENERATION
NUMERICAL SOLUTION
OXYGEN COMPOUNDS
POLLUTION
WATER
WATER POLLUTION