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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xin-Hui Shao & Jian-Rong Dong, 2024. "Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems," Mathematics, MDPI, vol. 12(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:375-:d:1325567
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