New Preconditioned Iteration Method Solving the Special Linear System from the PDE-Constrained Optimal Control Problem

In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used. We mainly solve the optimization problem by time-periodic eddy current in this paper. propose three-block splitting (TBS) iterative method proved that it is unconditionally convergent. At same time, corresponding TBS preconditioner derived from iteration method, we studied spectral properties preconditioned matrix. Finally, numerical examples two-dimensions applied to demonstrate advantages with Krylov subspace method.