Restrictive Preconditioning for Convection-Diffusion Distributed Control Problems

Restrictive Preconditioning for Convection-Diffusion Distributed Control Problems

Year:    2022

Author:    Wei Feng, Zeng-Qi Wang, Ruo-Bing Zhong, Galina V. Muratova

East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 233–246

Abstract

The restrictive preconditioning technique is employed in the preconditioned conjugate gradient and preconditioned Chebyshev iteration methods for the saddle point linear systems arising in convection-diffusion control problems. Utilizing an appropriate approximation of Schur complement, one obtains preconditioned matrix with eigenvalues located in the interval [1/2,1]. The convergence rate of the methods is studied. Unlike the restrictively preconditioned conjugate gradient method, the restrictively preconditioned Chebyshev iteration method is more tolerant to the inexact execution of the preconditioning. This indicates that the preconditioned Chebyshev iteration method is more practical when dealing with large scale linear systems. Theoretical and numerical results demonstrate that the iteration count of the solvers used do not depend the mesh size, the regularization parameter and on the Peclet number.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.080621.030921

East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 233–246

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Convection-diffusion distributed control problem restrictive preconditioning conjugate gradient method Chebyshev semi-iteration method.

Author Details

Wei Feng

Zeng-Qi Wang

Ruo-Bing Zhong

Galina V. Muratova