TY - JOUR
T1 - A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems
AU - Axelsson , Owe
AU - Khojasteh Salkuyeh , Davod
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1098
EP - 1122
PY - 2020
DA - 2020/06
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2020-0016
UR - https://global-sci.org/intro/article_detail/nmtma/16968.html
KW - Preconditioner, hybrid, PRESB, GMRES, PDE-constrained optimization, optimization.
AB - <p style="text-align: justify;">Optimal control problems constrained by a partial differential equation
(PDE) arise in various important applications, such as in engineering and natural
sciences. Normally the problems are of very large scale, so iterative solution methods must be used. Thereby the choice of an iteration method in conjunction with
an efficient preconditioner is essential. In this paper, we consider a new iteration
method and a new preconditioning technique for an elliptic PDE-constrained optimal control problem with a distributed control function. Some earlier used iteration
methods and preconditioners in the literature are compared, both analytically and
numerically with the new iteration method and the preconditioner.</p>