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Preconditioning convection dominated convectiondiffusion problems

Preconditioning convection dominated convectiondiffusion problems This paper is concerned with the numerical solution ofmultidimensional convection dominated convectiondiffusionproblems. These problems are characterized by a large parameter, K,multiplying the convection terms. The goal of this work is the developmentand analysis of effective preconditioners for iteratively solving the largesystem of linear equations arising from various finite element and finitedifference discretizations with grid size h. When centered finitedifference schemes and standard Galerkin finite element methods are used,h must be related to K by the stability constraint, Kh C0, where the constant C0 is sufficiently small. A class ofpreconditioners is developed that significantly reduces the condition numberfor large K and small h. Furthermore, these preconditioners areinexpensive to implement and well suited for parallel computation. It isshown that under suitable assumptions, the number of iterations remainsbounded as h 0 with K fixed and, at worst, grows slowly as K. Numerical results are presented illustrating the theory. Itis also shown how to apply the theoretical results to more generalconvectiondiffusion problems and alternative discretizationsincluding streamline diffusion methods that remain stable as Kh. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat and Fluid Flow Emerald Publishing

Preconditioning convection dominated convectiondiffusion problems

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References (18)

Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/EUM0000000004059
Publisher site
See Article on Publisher Site

Abstract

This paper is concerned with the numerical solution ofmultidimensional convection dominated convectiondiffusionproblems. These problems are characterized by a large parameter, K,multiplying the convection terms. The goal of this work is the developmentand analysis of effective preconditioners for iteratively solving the largesystem of linear equations arising from various finite element and finitedifference discretizations with grid size h. When centered finitedifference schemes and standard Galerkin finite element methods are used,h must be related to K by the stability constraint, Kh C0, where the constant C0 is sufficiently small. A class ofpreconditioners is developed that significantly reduces the condition numberfor large K and small h. Furthermore, these preconditioners areinexpensive to implement and well suited for parallel computation. It isshown that under suitable assumptions, the number of iterations remainsbounded as h 0 with K fixed and, at worst, grows slowly as K. Numerical results are presented illustrating the theory. Itis also shown how to apply the theoretical results to more generalconvectiondiffusion problems and alternative discretizationsincluding streamline diffusion methods that remain stable as Kh.

Journal

International Journal of Numerical Methods for Heat and Fluid FlowEmerald Publishing

Published: Feb 1, 1995

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