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<p>This work introduces an iterative method designed for saddle point systems with a nonsymmetric positive definite (1,1) block. The study investigates the conditions for both convergence and semi-convergence of the proposed method. Some characteristics of the induced preconditioner, including the distribution of eigenvalues of the preconditioned matrix, are discussed. The induced preconditioner is employed to expedite the convergence speed of the flexible version of GMRES method. Finally, numerical experiments based on test problems arising from finite element discretizations of the Stokes and Oseen equations are provided to demonstrate the effectiveness of the proposed preconditioner.</p>

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A Block Splitting Preconditioner for Nonsymmetric Saddle Point Problems

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Mehdi Makhdomi,
  • Morad Ahmadnasab,
  • Davod Khojasteh Salkuyeh,
  • Amjad Alipanah

摘要

This work introduces an iterative method designed for saddle point systems with a nonsymmetric positive definite (1,1) block. The study investigates the conditions for both convergence and semi-convergence of the proposed method. Some characteristics of the induced preconditioner, including the distribution of eigenvalues of the preconditioned matrix, are discussed. The induced preconditioner is employed to expedite the convergence speed of the flexible version of GMRES method. Finally, numerical experiments based on test problems arising from finite element discretizations of the Stokes and Oseen equations are provided to demonstrate the effectiveness of the proposed preconditioner.