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

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

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In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used.We mainly solve the optimization problem constrained by the time-periodic eddy current equation in this paper.We propose the three-block splitting (TBS) iterative method hancheng fashion and proved that it is unconditionally convergent.

At the same time, the corresponding TBS preconditioner is derived from the TBS iteration miami dolphins wordmark method, and we studied the spectral properties of the preconditioned matrix.Finally, numerical examples in two-dimensions is applied to demonstrate the advantages of the TBS iterative method and TBS preconditioner with the Krylov subspace method.