Applications of the PRESB Preconditioning Method for OPT-PDE Problems

0549527 - ÚGN 2022 RIV CH eng C - Conference Paper (international conference)
Axelsson, Owe
Applications of the PRESB Preconditioning Method for OPT-PDE Problems.
Lecture Notes in Computational Science and Engineering. Cham: Springer, 2021, s. 73-81. ISBN 978-3-030-55873-4. ISSN 1439-7358. E-ISSN 2197-7100.
[European Conference on Numerical Mathematics and Advanced Applications (ENUMATH). Egmond aan Zee (NL), 30.09.2019-04.10.2019]
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : optimal control problems * preconditioning * eigenvalues
OECD category: Applied mathematics
Method of publishing: Limited access
https://link.springer.com/chapter/10.1007%2F978-3-030-55874-1_6

Optimal control problems constrained by partial differential equations arise in a multitude of important applications. They lead mostly to the solution of very large scale algebraic systems to be solved, which must be done by iterative methods. The problems should then be formulated so that they can be solved fast and robust, which requires the construction of an efficient preconditioner. After reduction of a variable, a two-by-two block matrix system with square blocks arises for which such a preconditioner, PRESB is presented, involving the solution of two algebraic systems which are a linear combination of the matrix blocks. These systems can be solved by inner iterations, involving some available classical solvers to some relative, not very demanding tolerance.
Permanent Link: http://hdl.handle.net/11104/0325528