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

Yan-Ran Li, Xin-Hui Shao and Shi-Yu Li
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Yan-Ran Li: Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China
Xin-Hui Shao: Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China
Shi-Yu Li: Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China

Mathematics, 2021, vol. 9, issue 5, 1-13

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: time-periodic eddy current problem; iteration methods; preconditioner; generalized saddle point problem; PDE-constrained optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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