A robust structured preconditioner for the time-harmonic parabolic optimal control problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F18%3A00495413" target="_blank" >RIV/68145535:_____/18:00495413 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007%2Fs11075-017-0451-5.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs11075-017-0451-5.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-017-0451-5" target="_blank" >10.1007/s11075-017-0451-5</a>

Result language
angličtina
Original language name
A robust structured preconditioner for the time-harmonic parabolic optimal control problem
Original language description
We consider the iterative solution of optimal control problems constrained by the time-harmonic parabolic equations. Due to the time-harmonic property of the control equations, a suitable discretization of the corresponding optimality systems leads to a large complex linear system with special two-by-two block matrix of saddle point form. For this algebraic system, an efficient preconditioner is constructed, which results in a fast Krylov subspace solver, that is robust with respect to the mesh size, frequency, and regularization parameters. Furthermore, the implementation is straightforward and the computational complexity is of optimal order, linear in the number of degrees of freedom. We show that the eigenvalue distribution of the corresponding preconditioned matrix leads to a condition number bounded above by 2. Numerical experiments confirming the theoretical derivations are presented, including comparisons with some other existing preconditioners.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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