New Preconditioned Iteration Method Solving the Special Linear System from the PDE-Constrained Optimal Control Problem
Open Access
- 2 March 2021
- journal article
- research article
- Published by MDPI AG in Mathematics
- Vol. 9 (5), 510
- https://doi.org/10.3390/math9050510
Abstract
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 and proved that it is unconditionally convergent. At the same time, the corresponding TBS preconditioner is derived from the TBS iteration 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.Keywords
Funding Information
- Central University Basic Scientific Research Business Expenses Special Funds (N2005013)
- the Natural Science Foundation of Liaoning Province (20170540323)
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