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Additive block diagonal preconditioning for block two-by-two linear systems of skew-Hamiltonian coefficient matrices

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Abstract

For a class of block two-by-two systems of linear equations with certain skew-Hamiltonian coefficient matrices, we construct additive block diagonal preconditioning matrices and discuss the eigen-properties of the corresponding preconditioned matrices. The additive block diagonal preconditioners can be employed to accelerate the convergence rates of Krylov subspace iteration methods such as MINRES and GMRES. Numerical experiments show that MINRES preconditioned by the exact and the inexact additive block diagonal preconditioners are effective, robust and scalable solvers for the block two-by-two linear systems arising from the Galerkin finite-element discretizations of a class of distributed control problems.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, People’s Republic of China

    Zhong-Zhi Bai

  2. State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100190, People’s Republic of China

    Zhong-Zhi Bai

  3. Key Laboratory of Environmental Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Fang Chen

  4. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, People’s Republic of China

    Zeng-Qi Wang

Authors
  1. Zhong-Zhi Bai
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  2. Fang Chen
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  3. Zeng-Qi Wang
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Correspondence to Zhong-Zhi Bai.

Additional information

Supported by The National Natural Science Foundation for Creative Research Groups (No. 11021101), The Hundred Talent Project of Chinese Academy of Sciences, The National Basic Research Program (No. 2011CB309703), and The National Natural Science Foundation (No. 91118001 and No. 11001175), P.R. China.

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Bai, ZZ., Chen, F. & Wang, ZQ. Additive block diagonal preconditioning for block two-by-two linear systems of skew-Hamiltonian coefficient matrices. Numer Algor 62, 655–675 (2013). https://doi.org/10.1007/s11075-013-9696-9

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  • DOI: https://doi.org/10.1007/s11075-013-9696-9

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