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On the eigenvalues of the saddle point matrices discretized from Navier–Stokes equations

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Abstract

In this paper, we study the spectral distributions of the saddle point matrices arising from the discretization and linearization of the Navier–Stokes equations, where the (1,1) block is nonsymmetric positive definite. In this paper, we derive the lower and upper bounds of the real and imaginary parts of all the eigenvalues of the saddle point matrices. We then propose a new class of block triangle preconditioners for solving the saddle point problems, and analyze the spectral properties of the preconditioned systems. Some numerical experiments with the preconditioned restarted generalized minimal residual method are reported to demonstrate the effectiveness and feasibility of these block triangle preconditioners.

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Acknowledgements

This work was supported by National Postdoctoral Program for Innovative Talents (Grant No.BX201600182), China Postdoctoral Science Foundation (Grant No. 2016M600141) and Fujian Natural Science Foundation (Grant Nos. 2016J01005, 2015J01578).

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Authors and Affiliations

  1. College of Mathematics and Informatics, Fujian Key Laboratory of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou, 350117, China

    Na Huang & Chang-Feng Ma

  2. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Na Huang

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  1. Na Huang
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Correspondence to Chang-Feng Ma.

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Huang, N., Ma, CF. On the eigenvalues of the saddle point matrices discretized from Navier–Stokes equations. Numer Algor 79, 41–64 (2018). https://doi.org/10.1007/s11075-017-0427-5

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  • DOI: https://doi.org/10.1007/s11075-017-0427-5

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