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The influence of the order of fill‐in on the convergence rate for ILU preconditioned iterative solvers

S.Ø. Wille (Faculty of Engineering, Oslo University College, Oslo, Norway, Laborato´rio Nacional de Computac¸a˜o Cientifica, Petropolis, Brazil, ASE‐EM, TICAM, The University of Texas at Austin, USA)
Ø. Staff (Faculty of Engineering, Oslo University College, Oslo, Norway)
A.F.D. Loula (Laborato´rio Nacional de Computac¸a˜o Cientifica, Petropolis, Brazil)
G.F. Carey (ASE‐EM, TICAM, The University of Texas at Austin, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 1 April 2004

224

Abstract

The indefinite nature of the mixed finite element formulation of the Navier‐Stokes equations is treated by segregation of the variables. The segregation algorithm assembles the coefficients which correspond to the velocity variables in the upper part of the equation matrix and the coefficients which corresponds to the pressure variables in the lower part of the equation matrix. During the incomplete; elimination of the velocity matrix, fill‐in will occur in the pressure matrix, hence, divisions with zero are avoided. The fill‐in rule applied here is related to the location of the node in the finite element mesh, rather than the magnitude of the fill‐in or the magnitude of the coefficient at the location of the fill‐in. Different orders of fill‐in are explored for ILU preconditioning of the mixed finite element formulation of the Navier‐Stokes equations in two dimensions.

Keywords

Citation

Wille, S.Ø., Staff, Ø., Loula, A.F.D. and Carey, G.F. (2004), "The influence of the order of fill‐in on the convergence rate for ILU preconditioned iterative solvers", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 14 No. 3, pp. 325-340. https://doi.org/10.1108/09615530410517986

Publisher

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Emerald Group Publishing Limited

Copyright © 2004, Emerald Group Publishing Limited

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