Preconditioners for Time-Harmonic Optimal Control Eddy-Current Problems

0483094 - ÚGN 2019 RIV DE eng C - Conference Paper (international conference)
Axelsson, Owe - Lukáš, D.
Preconditioners for Time-Harmonic Optimal Control Eddy-Current Problems.
Lecture Notes in Computer Science. Berlin: Springer International Publishing AG, 2018, s. 47-54. Large-Scale Scientific Computing, 10665. ISBN 978-3-319-73440-8. ISSN 0302-9743. E-ISSN 1611-3349.
[LSSC 2017 - Large Scale Scientific Computing 2017 /11./. Sozopol (BG), 05.06.2017-09.06.2017]
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : preconditioning * Krylov subspace methods Optimal control * Eddy currents * time-harmonic
OECD category: Applied mathematics
https://link.springer.com/chapter/10.1007/978-3-319-73441-5_4

Time-harmonic formulations enable solution of time-dependent PDEs without use of normally slow time-stepping methods. Two efficient preconditioners for the discretized parabolic and eddy current
electromagnetic optimal control problems, one on block diagonal form and one utilizing the two by two block structure of the resulting matrix, are presented with simplified analysis and numerical illustrations. Both methods result in tight eigenvalue bounds for the preconditioned matrix and very few iterations that hold uniformly with respect to the mesh, problem and method parameters, with the exception of the dependence on reluctivity for the block diagonal preconditioner.
Permanent Link: http://hdl.handle.net/11104/0278504