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Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems - Poisson and convection-diffusion control
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SYSNO ASEP 0468119 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems - Poisson and convection-diffusion control Author(s) Axelsson, Owe (UGN-S) RID
Farouq, S. (SE)
Neytcheva, M. (SE)Number of authors 3 Source Title Numerical Algorithms. - : Springer - ISSN 1017-1398
Roč. 73, č. 3 (2016), s. 631-633Number of pages 33 s. Publication form Online - E Language eng - English Country NL - Netherlands Keywords PDE-constrained optimization problems ; finite elements ; iterative solution methods Subject RIV BA - General Mathematics R&D Projects ED1.1.00/02.0070 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UGN-S - RVO:68145535 UT WOS 000387113700003 EID SCOPUS 84959098100 DOI 10.1007/s11075-016-0111-1 Annotation 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. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2017 Electronic address http://link.springer.com/article/10.1007%2Fs11075-016-0111-1
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