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<p>This paper investigates the augmented Lagrangian shift-splitting (ALSS) preconditioner for the saddle point problems generated from the finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The convergence of the corresponding iteration method is proved and the spectral properties of the associated preconditioned saddle point matrix are studied. Theoretical analysis shows that all eigenvalues of the preconditioned matrix are strongly clustered. Differing from the existing preconditioners, the proposed preconditioner could be applied to the problem with the wave number being larger than 1. Finally, numerical experiments show the efficiency of the proposed preconditioner for Krylov subspace method.</p>

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Augmented Lagrangian shift-splitting preconditioner for saddle point problems and its applications to the discretized time-harmonic maxwell equations in mixed form

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Bo Wu,
  • Xing-bao Gao

摘要

This paper investigates the augmented Lagrangian shift-splitting (ALSS) preconditioner for the saddle point problems generated from the finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The convergence of the corresponding iteration method is proved and the spectral properties of the associated preconditioned saddle point matrix are studied. Theoretical analysis shows that all eigenvalues of the preconditioned matrix are strongly clustered. Differing from the existing preconditioners, the proposed preconditioner could be applied to the problem with the wave number being larger than 1. Finally, numerical experiments show the efficiency of the proposed preconditioner for Krylov subspace method.