A new iteration and preconditioning method for elliptic PDE-constrained optimization problems

0534435 - ÚGN 2021 RIV CN eng J - Journal Article
Axelsson, Owe - Salkuyeh, D.K.
A new iteration and preconditioning method for elliptic PDE-constrained optimization problems.
Numerical Mathematics. Roč. 13, č. 4 (2020), s. 1098-1122. ISSN 1004-8979. E-ISSN 2079-7338
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : preconditioner * hybrid * PRESB * GMRES * PDE-constrained optimization * optimization
OECD category: Applied mathematics
Impact factor: 1.210, year: 2020
Method of publishing: Limited access
http://www.global-sci.org/intro/article_detail/nmtma/16968.html

Optimal control problems constrained by a partial differential equation(PDE) arise in various important applications, such as in engineering and naturalsciences. Normally the problems are of very large scale, so iterative solution meth-ods must be used. Thereby the choice of an iteration method inconjunction withan efficient preconditioner is essential. In this paper, we consider a new iterationmethod and a new preconditioning technique for an elliptic PDE-constrained opti-mal control problem with a distributed control function. Some earlier used iterationmethods and preconditioners in the literature are compared, both analytically andnumerically with the new iteration method and the preconditioner.
Permanent Link: http://hdl.handle.net/11104/0312629