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

Xin-Hui Shao () and Jian-Rong Dong
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Xin-Hui Shao: Department of Mathematics, College of Sciences, Northeastern University, Shenyang 100098, China
Jian-Rong Dong: Department of Mathematics, College of Sciences, Northeastern University, Shenyang 100098, China

Mathematics, 2024, vol. 12, issue 3, 1-17

Abstract: 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.

Keywords: PDE-constrained optimization; Krylov subspace methods; eddy currents; preconditioner (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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