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Weighted graph based ordering techniques for preconditioned conjugate gradient methods (1995)

Clift, Simon S. ; Tang, Wei-Pai

Springer

BIT 35 (1995), S. 30-47

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ISSN: 1572-9125

Keywords: Conjugate gradient ; preconditioner ; matrix ordering ; weighted graph

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01732977

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Linear and non-linear iterative methods for the incompressible Navier-Stokes equations (1994)

Clift, Simon S. ; Forsyth, Peter A.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 18 (1994), S. 229-256

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ISSN: 0271-2091

Keywords: Navier-Stokes ; Non-linear iteration ; Preconditioned conjugate gradient ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: In this study, the discretized finite volume form of the two-dimensional, incompressible Navier-Stokes equations is solved using both a frozen coefficient and a full Newton non-linear iteration. The optimal method is a combination of these two techniques. The linearized equations are solved using a conjugate-gradient-like method (CGSTAB). Various types of preconditioning are developed. Completely general sparse matrix methods are used. Investigations are carried out to determine the effect of finite volume cell anisotropy on the preconditioner. Numerical results are given for several test problems.

Additional Material: 9 Ill.