TY - JOUR
T1 - A New Preconditioning Strategy for Solving a Class of Time-Dependent PDE-Constrained Optimization Problems
AU - Minli Zeng & Guofeng Zhang
JO - Journal of Computational Mathematics
VL - 3
SP - 215
EP - 232
PY - 2014
DA - 2014/06
SN - 32
DO - http://doi.org/10.4208/jcm.1401-CR3
UR - https://global-sci.org/intro/article_detail/jcm/9881.html
KW - PDE-constrained optimization, Reduced linear system of equations, Preconditioning, Saddle point problem, Krylov subspace methods.
AB - <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>