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A New Preconditioner with Two Variable Relaxation Parameters for Saddle Point Linear Systems with Highly Singular(1,1) Blocks

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DOI: 10.4236/ajcm.2011.14030    4,471 Downloads   7,898 Views  

ABSTRACT

In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Y. Zeng and C. Li, "A New Preconditioner with Two Variable Relaxation Parameters for Saddle Point Linear Systems with Highly Singular(1,1) Blocks," American Journal of Computational Mathematics, Vol. 1 No. 4, 2011, pp. 252-255. doi: 10.4236/ajcm.2011.14030.

References

[1] T. Z. Huang, G. H. Cheng and S. Q. Shen, “New Block Triangular Preconditioners for Saddle Point Linear Sys- tems with Highly Sigular (1,1) Blocks,” Compututer Phy- sics Communications, Vol. 180, No. 2, 2009, pp. 192-196.
[2] T. Rees and C. Grief, “A Preconditioner for Linear Sys- tems Arising from Interios Point Optimization Methods,” SIAM Journal of Scientific Computing, Vol. 29, No. 5, 2007, pp. 1992-2007. doi:10.1137/060661673
[3] S. Wright, “Stability of Augmented System Factoriza- tions in Intrerior-Point Methods,” SIAM Journal of Matrix Analysis and Applications, Vol. 18, No. 1, 1997, pp. 191-222. doi:10.1137/S0895479894271093
[4] V. Girault and P. Raviart, “Finite Elment methods for Na- vier-Stokes Equations,” Springer-Verlag, Berlin, 1986. doi:10.1007/978-3-642-61623-5
[5] C. Grief and D. Sch?tzau, “Preconditioners for Discretized Time-Harmonic Maxwell Equations in Mixed Form,” Nu- merical Linear Algebra with Applications, Vol. 14, No. 4, 2007, pp. 281-297. doi:10.1002/nla.515
[6] M. Benzi, G. H. Golub and J. Lieson, “Numerical Solution of Saddle Point Problems,” Acta Numerica, Vol. 14, 2005, pp.1-137. doi:10.1017/S0962492904000212
[7] G. H. Golub and C. Grief, “On Solving Block Structured Indefinite Linear Systems,” SIAM Journal of Scientific Computing, Vol. 24, No. 6, 2003, pp. 2076-2092. doi:10.1137/S1064827500375096
[8] C. Grief and D. Sch?tzau, “Preconditioners for Saddle point linear systems with highly singular (1,1) blocks, Electronic Transactions on Numerical Analysis, Vol. 22, 2006, pp. 114-121.
[9] P. Monk, “Finite Elements for Maxwell’s Quations,” Ox- frod University Press, New York, 2003.
[10] J. C. Nédélec, “A New Family of Mixed Finite Elements in ?3,” Numerische Mathematik, Vol. 50, No. 1, 1986, pp. 57-81. doi:10.1007/BF01389668

  
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