TY - JOUR
T1 - Restrictive Preconditioning for Convection-Diffusion Distributed Control Problems
AU - Feng , Wei
AU - Wang , Zeng-Qi
AU - Zhong , Ruo-Bing
AU - Muratova , Galina V.
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 233
EP - 246
PY - 2022
DA - 2022/02
SN - 12
DO - http://doi.org/10.4208/eajam.080621.030921
UR - https://global-sci.org/intro/article_detail/eajam/20252.html
KW - Convection-diffusion distributed control problem, restrictive preconditioning, conjugate gradient method, Chebyshev semi-iteration method.
AB - <p style="text-align: justify;">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.</p>