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

The influence of the order of fill‐in on the convergence rate for ILU preconditioned iterative... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

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

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Publisher
Emerald Publishing
Copyright
Copyright © 2004 Emerald Group Publishing Limited. All rights reserved.
ISSN
0961-5539
DOI
10.1108/09615530410517986
Publisher site
See Article on Publisher Site

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.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Apr 1, 2004

Keywords: Variational techniques; Operations management; Iterative methods; Finite element analysis

References

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