Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems - Poisson and convection-diffusion control

0468119 - ÚGN 2017 RIV NL eng J - Journal Article
Axelsson, Owe - Farouq, S. - Neytcheva, M.
Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems - Poisson and convection-diffusion control.
Numerical Algorithms. Roč. 73, č. 3 (2016), s. 631-633. ISSN 1017-1398. E-ISSN 1572-9265
R&D Projects: GA MŠMT ED1.1.00/02.0070
Institutional support: RVO:68145535
Keywords : PDE-constrained optimization problems * finite elements * iterative solution methods
Subject RIV: BA - General Mathematics
Impact factor: 1.241, year: 2016
http://link.springer.com/article/10.1007%2Fs11075-016-0111-1

Saddle point matrices of a special structure arise in optimal control problems. In this paper we consider distributed optimal control for various types of scalar stationary partial differential equations and compare the efficiency of several numerical solution methods. We 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 application of an efficient block matrix preconditioner that previously has been applied to solve complex-valued systems in real arithmetic. Under certain assumptions 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 elapsed time is favourably compared with other published methods.
Permanent Link: http://hdl.handle.net/11104/0265976