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 13 articles , 1 standard article )

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  1. Bommer, Vera; Yousept, Irwin: Optimal control of the full time-dependent Maxwell equations (2016)
  2. Hante, F.M.; Mommer, M.S.; Potschka, A.: Newton-Picard preconditioners for time-periodic parabolic optimal control problems (2015)
  3. Hoppe, Ronald H.W.; Yousept, Irwin: Adaptive edge element approximation of $H(\mathrmcurl$-elliptic optimal control problems with control constraints (2015)
  4. 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)
  5. Jia, ZhongXiao: On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems (2013)
  6. Kolmbauer, Michael: Efficient solvers for multiharmonic eddy current optimal control problems with various constraints and their analysis (2013)
  7. Kolmbauer, Michael; Langer, Ulrich: Efficient solvers for some classes of time-periodic eddy current optimal control problems (2013)
  8. Kolmbauer, Michael; Langer, Ulrich: A robust preconditioned MinRes solver for time periodic eddy current problems (2013)
  9. Krendl, Wolfgang; Simoncini, Valeria; Zulehner, Walter: Stability estimates and structural spectral properties of saddle point problems (2013)
  10. Kolmbauer, Michael: A robust FEM-BEM minres solver for distributed multiharmonic eddy current optimal control problems in unbounded domains (2012)
  11. Kolmbauer, Michael; Langer, Ulrich: A robust preconditioned minres solver for distributed time-periodic eddy current optimal control problems (2012)
  12. Kolmbauer, Michael; Langer, Ulrich: A frequency-robust solver for the time-harmonic eddy current problem (2012)
  13. Yousept, Irwin: Finite element analysis of an optimal control problem in the coefficients of time-harmonic eddy current equations (2012)