稀疏近似逆与多层块ILU预条件技术

谷同祥; 迟学斌; 刘兴平

稀疏近似逆与多层块ILU预条件技术

1.
北京应用物理与计算数学研究所计算物理实验室,北京8009信箱,北京 100088;2.中科院计算机网络信息中心超级计算中心,北京349信箱,北京 100080

基金项目: 国家自然科学基金资助项目(60373015);国家高技术研究发展计划基金资助项目(2001AA111043);计算物理国家重点实验室资助项目

详细信息

作者简介:
谷同祥(1964- ),男,汉族,河南焦作人,副研究员,博士(联系人.Tel:+86-10-62014411-2967;Fax:+86-10-62057289;E-mail:txgu@iapcm.ac.cn).

中图分类号: O241.6
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出版历程
- 收稿日期: 2002-05-28
- 修回日期: 2004-03-30
- 刊出日期: 2004-09-15

AINV and BILUM Preconditioning Techniques

1.
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, P. R. China;

摘要

摘要: 设计了一种求解一般稀疏线性方程组的健壮且有效的可并行化预条件子，这种预条件子涉及在多层块ILU预条件子(BILUM)中使用稀疏近似逆(AINV)技术．所得的预条件子保持了BILUM的健壮性，它比标准的BILUM预条件子有两点优势：控制稀疏性的能力和增强了并行性．数值例子显示了新预条件子的有效性和效率．
- 稀疏矩阵 /
- 预条件技术 /
- BILUM /
- AINV /
- Krylov子空间方法
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 re tains 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.
- sparse matrix /
- preconditioning technique /
- BILUM /
- AINV /
- Krylov subspace method

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参考文献(23)

[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. doi: 10.1137/S106482759732753X
[4]	Benzi M,Tuma M.A sparse approximate inverse preconditioner for nonsymmetric linear systems[J].SIAM J Sci Comput,1998,19(3):968—994. doi: 10.1137/S1064827595294691
[5]	Chan T F.TANG Wei-pai,Wan W L.Wavelet sparse approximate inverse preconditioners[J].BIT, 1997,37(3):644—660. doi: 10.1007/BF02510244
[6]	Chow E,Saad Y.Approximate inverse techniques for block-partitioned matrices[J].SIAM J Sci Comput,1997,18(6):1657—1675. doi: 10.1137/S1064827595281575
[7]	Chow E,Saad Y.Approximate inverse preconditioner via sparse-sparse iterations[J].SIAM J Sci Comput,1998,19(3):995—1023. doi: 10.1137/S1064827594270415
[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. doi: 10.1137/S1064827595288425
[9]	Grote M,Huckle T.Parallel preconditioning with sparse approximate inverses[J].SIAM J Sci Comput,1997,18(3):838—853. doi: 10.1137/S1064827594276552
[10]	Saad Y.ILUT: a dual threshold incomplete ILU preconditioner[J].Numer Linear Algebra Appl,1994,1(4):387—402. doi: 10.1002/nla.1680010405
[11]	TANG Wei-pai,Wan W L.Sparse approximate inverse smoother for multigrid[J].SIAM J Matrix Anal Appl,2000,21(4):1236—1252. doi: 10.1137/S0895479899339342
[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. doi: 10.1016/S0377-0427(99)00388-X
[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. doi: 10.1016/S0168-9274(99)00047-1
[14]	Benzi M,Tuma M.A comparative study of sparse approximate inverse preconditioners[J].Appl Numer Math,1999,30(2/3):305—340. doi: 10.1016/S0168-9274(98)00118-4
[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. doi: 10.1137/S1064827594271421
[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. doi: 10.1137/S1064827599356900
[17]	Benzi M,Tuma M.Orderings for factorized sparse approximate inverse preconditioners[J].SIAM J Sci Comput,2000,21(5):1851—1868. doi: 10.1137/S1064827598339372
[18]	Kolotina L Y,Yeremin A Y.Factorized sparse approximate inverse preconditioningⅠ: theory[J].SIAM J Matrix Anal Appl,1993,14(1):45—58. doi: 10.1137/0614004
[19]	Saad Y.ILUM:a multi-elimination ILU preconditioner for general sparse matrices[J].SIAM J Sci Comput,1996,17(4):830—847. doi: 10.1137/0917054
[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. doi: 10.1137/0914028
[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. doi: 10.1137/S0895479898341268
[23]	ZHANG Jun.On convergence of iterative methods with a fourth-order compact scheme[J].Appl Math Lett,1997,10(2):49—55.

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文章访问数: 2657
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稀疏近似逆与多层块ILU预条件技术

作者简介:
谷同祥(1964- ),男,汉族,河南焦作人,副研究员,博士(联系人.Tel:+86-10-62014411-2967;Fax:+86-10-62057289;E-mail:txgu@iapcm.ac.cn).

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AINV and BILUM Preconditioning Techniques

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留言板

稀疏近似逆与多层块ILU预条件技术

作者简介: 谷同祥(1964- ),男,汉族,河南焦作人,副研究员,博士(联系人.Tel:+86-10-62014411-2967;Fax:+86-10-62057289;E-mail:txgu@iapcm.ac.cn).

计量

出版历程

AINV and BILUM Preconditioning Techniques

计量

出版历程

目录

作者简介:
谷同祥(1964- ),男,汉族,河南焦作人,副研究员,博士(联系人.Tel:+86-10-62014411-2967;Fax:+86-10-62057289;E-mail:txgu@iapcm.ac.cn).