Efficient solvers for multiharmonic eddy current optimal control problems with various constraints and their analysis

This work is devoted to the multiharmonic analysis of eddy current optimal control problems in a time-periodic setting. In contrast to previous approaches, we derive the problem setting in a mixed variational formulation to enforce Coulomb gauge in an explicit way. Additionally, we include the cases of different control and observation domains, observation in certain energy spaces, observation at a final time and constraints to the control and the state. In all these cases, we propose a new preconditioned MinRes solver for the frequency domain equations and show that this solver is robust with respect to the space and time discretization parameters. In some cases, we can also show robustness with respect to the involved model, cost and regularization parameters. Numerical examples will be studied in a forthcoming paper.