Abstract
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.
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