AINV AND BILUM PRECONDITIONING TECHNIQUES

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (9): 1012-1021.

• Articles • Previous Articles Next Articles

AINV AND BILUM PRECONDITIONING TECHNIQUES

GU Tong-xiang^1,2, CHI Xue-bin², LIU Xing-ping¹

1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P. R. China;
2. Supercomputing Center of Computer Network Information Center, Chinese Academy of Science, P.O. Box 349, Beijing 100080, P. R. China

Received:2002-05-28 Revised:2004-03-30 Online:2004-09-18 Published:2004-09-18
Supported by:
the National Natural Science Foundation of China(60373015);the State Hi Tech Research and Development Program of China(2001AA111043);the Foundation of State Key Labora tory of Computational Physics

Abstract

Abstract: It was proposed that a robust and efficient parallelizable preconditioner for solving general sparse linear systems of equations, in which the use of sparse approximate inverse (AINV) techniques in a multi-level block ILU (BILUM) preconditioner were investigated. The resulting preconditioner retains robustness of BILUM preconditioner and has two advantages over the standard BILUM preconditioner: the ability to control sparsity and increased parallelism. Numerical experiments are used to show the effectiveness and efficiency of the new preconditioner.

Key words: sparse matrix, preconditioning technique, BILUM, AINV, Krylov subspace method

2010 MSC Number:

O241.6

GU Tong-xiang;CHI Xue-bin;LIU Xing-ping. AINV AND BILUM PRECONDITIONING TECHNIQUES. Applied Mathematics and Mechanics (English Edition), 2004, 25(9): 1012-1021.

TrendMD

References

[1] Saad Y.Iterative Methods for Sparse Linear Systems[M].New York:PWS Publishing, 1996.
[2] Golub G H,van der Vorst H A.Closer to the solution: iterative linear solver[A].In:Duff I S,Watson G A Eds.The State of the Art in Numerical Analysis[C] :Oxford: Clarendon Press,1997,63-92.
[3] Saad Y,ZHANG Jun.BILUM: block versions of multi-elimination and multi-level ILU preconditioner for general sparse linear systems[J].SIAM J Sci Comput,1999,20(6):2103-2121.
[4] Benzi M,Tuma M.A sparse approximate inverse preconditioner for nonsymmetric linear systems[J].SIAM J Sci Comput,1998,19(3):968-994.
[5] Chan T F.TANG Wei-pai,Wan W L.Wavelet sparse approximate inverse preconditioners[J].BIT, 1997,37(3):644-660.
[6] Chow E,Saad Y.Approximate inverse techniques for block-partitioned matrices[J].SIAM J Sci Comput,1997,18(6):1657-1675.
[7] Chow E,Saad Y.Approximate inverse preconditioner via sparse-sparse iterations[J].SIAM J Sci Comput,1998,19(3):995-1023.
[8] Gould N I M.Scott J A.Sparse approximate-inverse preconditioners using norm minimization techniques[J].SIAM J Sci Comput,1998,19(2):605-625.
[9] Grote M,Huckle T.Parallel preconditioning with sparse approximate inverses[J].SIAM J Sci Comput,1997,18(3):838-853.
[10] Saad Y.ILUT: a dual threshold incomplete ILU preconditioner[J].Numer Linear Algebra Appl,1994,1(4):387-402.
[11] TANG Wei-pai,Wan W L.Sparse approximate inverse smoother for multigrid[J].SIAM J Matrix Anal Appl,2000,21(4):1236-1252.
[12] Saad Y,ZHANG Jun.Enhanced multi-level block ILU preconditioning strategies for general linear systems[J].J Comput Appl Math,2001,130(1/2):99-118.
[13] ZHANG Jun.Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices[J].Appl Numer Math,2000,35(1):67-86.
[14] Benzi M,Tuma M.A comparative study of sparse approximate inverse preconditioners[J].Appl Numer Math,1999,30(2/3):305-340.
[15] Benzi M,Meyer C D,Tuma M.A sparse approximate inverse preconditioner for the conjugate gradient method[J].SIAM J Sci Comput,1996,17(5):1135-1149.
[16] Benzi M,Cullum J K,Tuma M.Robust approximate inverse preconditioning for the conjugate gradient method[J].SIAM J Sci Comput,2000,22(4):1318-1332.
[17] Benzi M,Tuma M.Orderings for factorized sparse approximate inverse preconditioners[J].SIAM J Sci Comput,2000,21(5):1851-1868.
[18] Kolotina L Y,Yeremin A Y.Factorized sparse approximate inverse preconditioningⅠ: theory[J].SIAM J Matrix Anal Appl,1993,14(1):45-58.
[19] Saad Y.ILUM:a multi-elimination ILU preconditioner for general sparse matrices[J].SIAM J Sci Comput,1996,17(4):830-847.
[20] Saad Y,Sosonkina M,ZHANG Jun.Domain decomposition and multi-level type techniques for general sparse linear systems[A].In:Mandel J,Farhat C,Cai X C,Eds.Domain Decomposition Methods 10[C].number 218 in Contemporary Mathematics, Providence, RI, AMS,1998,174-190.
[21] Saad Y.A flexible inner-outer preconditioned GMRES algorithm[J].SIAM J Sci Comput,1993,14(2):461-469.
[22] Saad Y,ZHANG Jun.BILUTM:a domain-based multi-level block ILUT preconditioner for general linear systems[J].SIAM J Matrix Anal Appl,1999,21(1):279-299.
[23] ZHANG Jun.On convergence of iterative methods with a fourth-order compact scheme[J].Appl Math Lett,1997,10(2):49-55.

AINV AND BILUM PRECONDITIONING TECHNIQUES

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 2

Recommended Articles

Metrics

Comments

[1]	Feng WU;Qiang GAO;Wan-xie ZHONG. Fast precise integration method for hyperbolic heat conduction problems [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(7): 791-800.
[2]	Liu Xiaoming;Lu Zhiming;Liu Yulu . KRYLOV SUBSPACE PROJECTION METHOD AND ITS APPLICATION ON OIL RESERVOIR SIMULATION [J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(6): 607-616.