@Article{JCM-32-215,
author = {Minli Zeng and Guofeng Zhang},
title = {A New Preconditioning Strategy for Solving a Class of Time-Dependent PDE-Constrained Optimization Problems},
journal = {Journal of Computational Mathematics},
year = {2014},
volume = {32},
number = {3},
pages = {215--232},
abstract = {<p style="text-align: justify;">In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distributed control problem involving the heat equation with two different functions. First a natural order-reduction is performed, and then the reduced-order linear system of equations is solved by the preconditioned MINRES algorithm with a new preconditioning techniques. The spectral properties of the preconditioned matrix are analyzed. Numerical results demonstrate that the preconditioning strategy for solving the large sparse systems discretized from the time-dependent problems is more effective for a wide range of mesh sizes and the value of the regularization parameter.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1401-CR3},
url = {http://global-sci.org/intro/article_detail/jcm/9881.html}
}