Preconditioned Conjugate Gradient and Multigrid Methods for Numerical Solution of Multicomponent Mass Transfer Equations I. Diffusion-Reaction Equations

In a series of two papers, we analyze the numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) and multigrid method in solving two-dimensional multicomponent mass transfer equations. The present test problems are steady-state, linear and nonlinear diffusion...

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Bibliographic Details
Published in:Numerical heat transfer. Part A, Applications Vol. 66; no. 11; pp. 1268 - 1296
Main Authors: Juncu, Gheorghe, Nicola, Aurelian, Popa, Constantin, Stroila, Elena
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 01.12.2014
Taylor & Francis Ltd
Subjects:
Algorithms
Conjugate gradients
Differential equations
Diffusion-reaction equations
Heat transfer
Mass transfer
Mathematical analysis
Mathematical models
Multigrid methods
Nonlinearity
Numerical analysis
ISSN:1040-7782, 1521-0634
Online Access:Get full text
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Summary:In a series of two papers, we analyze the numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) and multigrid method in solving two-dimensional multicomponent mass transfer equations. The present test problems are steady-state, linear and nonlinear diffusion-reaction equations. The nonlinear algorithm used in connection with the preconditioned conjugate gradient methods is the modified Picard iteration. Theoretical results about the preconditioning are presented. The multigrid algorithm used is the Full Approximation Storage algorithm. The finite difference method was used to discretize the mathematical model equations. The numerical results obtained show good numerical performances.
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ISSN:1040-7782
1521-0634
DOI:10.1080/10407782.2014.915674