Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

0482333 - ÚGN 2018 RIV NL eng J - Journal Article
Axelsson, Owe - Farouq, S. - Neytcheva, M.
Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems.
Numerical Algorithms. Roč. 74, č. 1 (2017), s. 19-37. ISSN 1017-1398. E-ISSN 1572-9265
Institutional support: RVO:68145535
Keywords : PDE-constrained optimization problems * finite elements * iterative solution methods * preconditioning
OECD category: Applied mathematics
Impact factor: 1.536, year: 2017
https://link.springer.com/article/10.1007%2Fs11075-016-0136-5

The governing dynamics of fluid flow is stated as a system of partial differential equations referred to as the Navier-Stokes system. In industrial and scientific applications, fluid flow control becomes an optimization problem where the governing partial differential equations of the fluid flow are stated as constraints. When discretized, the optimal control of the Navier-Stokes equations leads to large sparse saddle point systems in two levels. In this paper, we consider distributed optimal control for the Stokes system and test the particular case when the arising linear system can be compressed after eliminating the control function. In that case, a system arises in a form which enables the application of an efficient block matrix preconditioner that previously has been applied to solve complex-valued systems in real arithmetic. Under certain conditions, the condition number of the so preconditioned matrix is bounded by 2. The numerical and computational efficiency of the method in terms of number of iterations and execution time is favorably compared with other published methods.
Permanent Link: http://hdl.handle.net/11104/0277747