A note on preconditioning methods for time-periodic eddy current optimal control problems

0509838 - ÚGN 2020 RIV NL eng J - Článek v odborném periodiku
Axelsson, Owe - Liang, Z.-Z.
A note on preconditioning methods for time-periodic eddy current optimal control problems.
Journal of Computational and Applied Mathematics. Roč. 352, May 2019 (2019), s. 262-277. ISSN 0377-0427. E-ISSN 1879-1778
Grant CEP: GA MŠMT LQ1602; GA MŠMT LD15105
Institucionální podpora: RVO:68145535
Klíčová slova: PDE-constrained optimization * time-periodic eddy current problem * preconditioning * spectral analysis
Obor OECD: Applied mathematics
Impakt faktor: 2.037, rok: 2019
Způsob publikování: Omezený přístup
https://www.sciencedirect.com/science/article/pii/S0377042718306757

In this paper, iterative solution of optimal control problems constrained by the time-periodic eddy current equations is considered. Two methods for time-harmonic parabolic optimal control problem are further analyzed for solving the complex valued linear systems arising from the edge element discretization process. For both methods, we give preconditioners with eigenvalue distribution results showing that the eigenvalues of the corresponding preconditioned matrices are located in tight intervals away from the origin. Numerical experiments based on 2D and 3D problems show that the two methods coupled with a Krylov subspace acceleration have robust performance with respect to the mesh size, frequency and regularization parameters which enables a numerical comparison of the methods for a wide variety of parameter values.
Trvalý link: http://hdl.handle.net/11104/0300452