Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems

In this paper, we consider the numerical solution of a large complex linear system with a saddle-point form obtained by the discretization of the time-harmonic eddy-current optimal control problem. A new Schur complement is proposed for this algebraic system, extending it to both the block-triangular preconditioner and the structured preconditioner. A theoretical analysis proves that the eigenvalues of block-triangular and structured preconditioned matrices are located in the interval [1/2, 1]. Numerical simulations show that two new preconditioners coupled with a Krylov subspace acceleration have good feasibility and effectiveness and are superior to some existing efficient algorithms.