MinRes

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 29 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. Wolfmayr, Monika: Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems (2020)
  3. Axelsson, Owe; Lukáš, Dalibor: Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems (2019)
  4. Nestler, Peter; Schlömer, Nico; Klein, Olaf; Sprekels, Jürgen; Tröltzsch, Fredi: Optimal control of semiconductor melts by traveling magnetic fields (2019)
  5. Axelsson, Owe; Lukáš, Dalibor: Preconditioners for time-harmonic optimal control eddy-current problems (2018)
  6. Liang, Zhao-Zheng; Axelsson, Owe; Neytcheva, Maya: A robust structured preconditioner for time-harmonic parabolic optimal control problems (2018)
  7. Liao, Li-Dan; Zhang, Guo-Feng; Zhang, Lei: Robust preconditioners for optimal control with time-periodic parabolic equation (2018)
  8. Tröltzsch, Fredi; Valli, Alberto: Optimal voltage control of non-stationary Eddy current problems (2018)
  9. Nicaise, Serge; Tröltzsch, Fredi: Optimal control of some quasilinear Maxwell equations of parabolic type (2017)
  10. Yousept, Irwin; Zou, Jun: Edge element method for optimal control of stationary Maxwell system with Gauss law (2017)
  11. Bommer, Vera; Yousept, Irwin: Optimal control of the full time-dependent Maxwell equations (2016)
  12. Zheng, Zhong; Zhang, Guo-Feng; Zhu, Mu-Zheng: A note on preconditioners for complex linear systems arising from PDE-constrained optimization problems (2016)
  13. Hante, F. M.; Mommer, M. S.; Potschka, A.: Newton-Picard preconditioners for time-periodic parabolic optimal control problems (2015)
  14. Hoppe, Ronald H. W.; Yousept, Irwin: Adaptive edge element approximation of (H(\mathrmcurl)-elliptic optimal control problems with control constraints (2015)
  15. Langer, Ulrich; Repin, Sergey; Wolfmayr, Monika: Functional a posteriori error estimates for parabolic time-periodic boundary value problems (2015)
  16. Nicaise, Serge; Stingelin, Simon; Tröltzsch, Fredi: Optimal control of magnetic fields in flow measurement (2015)
  17. Zheng, Zhong; Zhang, Guo-Feng; Zhu, Mu-Zheng: A block alternating splitting iteration method for a class of block two-by-two complex linear systems (2015)
  18. Nicaise, Serge; Stingelin, Simon; Tröltzsch, Fredi: On two optimal control problems for magnetic fields (2014)
  19. Jia, ZhongXiao: On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems (2013)
  20. Kollmann, Markus; Kolmbauer, Michael: A preconditioned MinRes solver for time-periodic parabolic optimal control problems. (2013)

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