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A SPECIAL PARAMETERIZED INEXACT UZAWA ALGORITHM FOR SYMMETRIC SADDLE POINT PROBLEM

ABSTRACT
In this paper, we consider a symmetric saddle point problem arising in the fluid dynamics. A special parameterized inexact Uzawa algorithm is proposed for solving the symmetric saddle point problem. The convergence of this special algorithm is considered. Sufficient conditions for the convergence are given. Numerical experiments resulting from stokes problem are presented to show the efficiency of the algorithm.
KEYWORDS
PAPER SUBMITTED: 2017-01-25
PAPER REVISED: 2017-12-16
PAPER ACCEPTED: 2017-12-16
PUBLISHED ONLINE: 2018-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI1804715L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE 4, PAGES [1715 - 1721]
REFERENCES
  1. Elman, H. C., et al., Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics, Numerical Mathematics and Scientific Computation, Oxford University Press, New York, USA, 2005
  2. Silvester, D., Wathen, A., Fast Iterative Solution of Stabilised Stokes Systems, Part II: Using General Block Preconditioners, SIAM Journal on Numerical Analysis, 31 (1994), 5, pp. 1352-1367
  3. Hristov, J., Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid, Thermal Science, 16 (2012), 2, pp. 395-410
  4. Qiu, Y. Y., Solving a Class of Boundary Value Problems by LSQR, Thermal Science, 21 (2017), 4, pp. 1719-1724
  5. Boiti, M., et al., Integrable Two-Dimensional Generalization of the Sine-and Sinh-Gordon Equations, Inverse Problems, 3 (1987), 1, pp. 37-49
  6. Bai, Z. Z., Wang, Z. Q., On Parameterized Inexact Uzawa Methods for Generalized Saddle Point Prob-lems, Linear Algebra and its Applications, 428 (2008), 11-12, pp. 2900-2932
  7. Bramble, J. H., et al., Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems, SIAM Jour-nal on Numerical Analysis, 34 (1997), 3, pp. 1072-1092
  8. Lu, J. F., Zhang, Z. Y., A Modified Nonlinear Inexact Uzawa Algorithm with a Variable Relaxation Pa-rameter for the Stabilized Saddle Point Problem, SIAM Journal on Matrix Analysis and Applications, 31 (2010), 4, pp. 1934-1957
  9. Chen, X. J., On Preconditioned Uzawa Methods and SOR Methods for Saddle-Point Problems, Journal of Computational & Applied Mathematics, 100 (1998), 2, pp. 207-224
  10. Bai, Z. Z., et al., Preconditioned Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Semidefinite Linear Systems, Numerische Mathematik, 98 (2004), 1, pp. 1-32
  11. Benzi, M., Golub, G. H., A Preconditioner for Generalized Saddle Point Problems, SIAM Journal on Matrix Analysis and Applications, 26 (2004), 1, pp. 20-41
  12. Benzi, M., et al., Numerical Solution of Saddle Point Problems, Acta Numerica, 14 (2005), May, pp. 1-137
  13. Zhou, Y. Y., Zhang, G. F., A Generalization of Parameterized Inexact Uzawa Method for Generalized Saddle Point Problems, Applied Mathematics and Computation, 215 (2009), 2, pp. 599-607
  14. Dou, Q. Y., Yin, J. F., A Class of Generalized Inexact Uzawa Methods for Saddle Point Problems, Mathematica Numerica Sinica, 34 (2011), 1, pp. 37-48
  15. Young, D. M., Iterative Solution for Large Linear Systems, Academic Press, New York, USA, 1971
  16. Elman, H. C., et al., Algorithm 866: IFISS, a Matlab Toolbox for Modelling Incompressible Flow, ACM Transactions on Mathematical Software, 33 (2007), 2, pp. 1-18

© 2018 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence