A robust FEM-BEM minres solver for distributed multiharmonic eddy current optimal control problems in unbounded domains. This work is devoted to distributed optimal control problems for multiharmonic eddy current problems in unbounded domains. We apply a multiharmonic approach to the optimality system and discretize in space by means of a symmetrically coupled finite and boundary element method, taking care of the different physical behavior in conducting and non-conducting subdomains, respectively. We construct and analyze a new preconditioned MinRes solver for the system of frequency domain equations. We show that this solver is robust with respect to the space discretization and time discretization parameters as well as the involved “bad” parameters like the conductivity and the regularization parameters. Furthermore, we analyze the asymptotic behavior of the error in terms of the discretization parameters for our special discretization scheme.

References in zbMATH (referenced in 36 articles , 1 standard article )

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  1. Axelsson, Owe; Liang, Zhao-Zheng; Kruzik, Jakub; Horak, David: Inner product free iterative solution and elimination methods for linear systems of a three-by-three block matrix form (2021)
  2. Liang, Zhao-Zheng; Zhang, Guo-Feng: Robust preconditioning techniques for multiharmonic finite element method with application to time-periodic parabolic optimal control problems (2021)
  3. Mirchi, Hamid; Salkuyeh, Davod Khojasteh: A new iterative method for solving the systems arisen from finite element discretization of a time-harmonic parabolic optimal control problems (2021)
  4. Zeng, Min-Li: Respectively scaled splitting iteration method for a class of block 4-by-4 linear systems from eddy current electromagnetic problems (2021)
  5. Zeng, Min-Li: A circulant-matrix-based new accelerated GSOR preconditioned method for block two-by-two linear systems from image restoration problems (2021)
  6. Axelsson, Owe; Karátson, János: Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks (2020)
  7. Wolfmayr, Monika: Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems (2020)
  8. Wu, Shu-Lin; Zhou, Tao: Diagonalization-based parallel-in-time algorithms for parabolic PDE-constrained optimization problems (2020)
  9. Axelsson, Owe; Lukáš, Dalibor: Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems (2019)
  10. Nestler, Peter; Schlömer, Nico; Klein, Olaf; Sprekels, Jürgen; Tröltzsch, Fredi: Optimal control of semiconductor melts by traveling magnetic fields (2019)
  11. Axelsson, Owe; Lukáš, Dalibor: Preconditioners for time-harmonic optimal control eddy-current problems (2018)
  12. Axelsson, Owe; Neytcheva, Maya; Liang, Zhao-Zheng: Parallel solution methods and preconditioners for evolution equations (2018)
  13. Liang, Zhao-Zheng; Axelsson, Owe; Neytcheva, Maya: A robust structured preconditioner for time-harmonic parabolic optimal control problems (2018)
  14. Liao, Li-Dan; Zhang, Guo-Feng; Zhang, Lei: Robust preconditioners for optimal control with time-periodic parabolic equation (2018)
  15. Tröltzsch, Fredi; Valli, Alberto: Optimal voltage control of non-stationary Eddy current problems (2018)
  16. Nicaise, Serge; Tröltzsch, Fredi: Optimal control of some quasilinear Maxwell equations of parabolic type (2017)
  17. Yousept, Irwin; Zou, Jun: Edge element method for optimal control of stationary Maxwell system with Gauss law (2017)
  18. Bommer, Vera; Yousept, Irwin: Optimal control of the full time-dependent Maxwell equations (2016)
  19. Zheng, Zhong; Zhang, Guo-Feng; Zhu, Mu-Zheng: A note on preconditioners for complex linear systems arising from PDE-constrained optimization problems (2016)
  20. Hante, F. M.; Mommer, M. S.; Potschka, A.: Newton-Picard preconditioners for time-periodic parabolic optimal control problems (2015)

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