Krylov子空间投影法及其在油藏数值模拟中的应用

刘晓明; 卢志明; 刘宇陆

Krylov子空间投影法及其在油藏数值模拟中的应用

上海市应用数学和力学研究所, 上海大学, 上海 200072

基金项目: 国家自然科学基金资助项目(19872043)

详细信息

作者简介:
刘晓明(1950~ ),男,上海人,副研究员,校长助理.

中图分类号: O241.6
计量
- 文章访问数: 2847
- HTML全文浏览量: 179
- PDF下载量: 724
- 被引次数: 0
出版历程
- 收稿日期: 1999-03-15
- 修回日期: 1999-12-10
- 刊出日期: 2000-06-15

Krylov Subspace Projection Method and ItsApplication on Oil Reservoir Simulation

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China

摘要

摘要: Krylov子空间投影法是一类非常有效的大型线性代数方程组解法,随着左右空间L_m、K_m的不同选取可以得到许多人们熟知的方法.按矩阵H_m的不同类型,将Krylov子空间方法分成两大类,简要分析了这两类方法的优缺点及其最新进展.将目前最为可靠实用的广义最小余量法(GMRES)应用于油藏数值模拟计算问题,利用矩阵分块技术,采用块拟消去法(PE)对系数阵进行预处理.计算结果表明本文的预处理GMRES方法优于目前使用较多的预处理正交极小化ORTHMIN方法,最后还讨论了投影类方法的局限和今后的可能发展方向.
- Krylov子空间投影法 /
- 块拟消去法 /
- 油藏数值模拟
Abstract: Krylov subspace projection methods are known to be highly efficient for solving large linear systems.Many different versions arise from different choices to the left and right subspaces.These methods were classified into two groups in terms of the different forms of matrix H_m,the main properties in applications and the new versions of these two types of methods were briefly reviewed,then one of the most efficient versions,GMRES method was applied to oil reservoir simulation.The block Pseudo-Elinimation method was used to generate the preconditioned matrix.Numerical results show much better performance of this preconditioned techniques and the GMRES method than that of preconditioned ORTHMIN method,which is now in use in oil reservoir simulation.Finally,some limitations of Krylov subspace methods and some potential improvements to this type of methods are furtherly presented.
- Krylov subspace methods /
- block PE method /
- numerical oil reservoir simulation

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参考文献(23)

[1]	Saad Y.Krylov subspace methods for solving large unsymmetric linear systems[J].Mathematics of Computations,1981,37(155):105~126.
[2]	Saad Y,Schultz M A.Conjugate gradient-like algorithm for solving nonsymmetric linear systems[J].Mathematics of Computations,1985,44(170):417~424.
[3]	Saad Y,Schultz M A.GMRES:A generalized minimum residual algorithm for solving nonsymmetric linear systems[J].SIAM J Sci Comput,1986,7(3):859~869.
[4]	Brown P N.A theoretical comparision of the ARNOLDI and GMRES algorithms[J].SIAM J Sci Comput,1991,12(1):58~78.
[5]	Desa C,Irani K M,Ribbens C J,et al.Preconditioned iterative methods for homotopy curve trackling[J].SIAM J Sci Comput,1992,13(1):30~45.
[6]	Ern A,Giovangigli V,Keyes D E,et al.Towards polyalgorithm linear system solvers for nonlinear elliptic problems[J].SIAM J Sci Comput,1994,15(3):681~703.
[7]	卢志明.油藏数值模拟中的一种新方法[D].硕士论文.上海:复旦大学,1993.
[8]	Tan L H,Bathe K J.Studies of finite element procedures-the conjugate gradient and GMRES methods in ADINA and ADINA-F[J].Computers &Structure,1991,40(2):441~449.
[9]	Frommer A,Glassner U.Restarted GMRES for the shifted linear systems[J].SIAM J Sci Comput,1998,19(1):15~26.
[10]	Paige C C,Saunders M A.Solution of sparse indefinite systems of linear equations[J].SIAM J Numer Anal,1975,12(4):617~629.
[11]	Sonneveld P.CGS,a fast Lanczos-type solver for nonsymmetric linear system[J].SIAM J Sci Statist Comput,1989,10(1):36~52.
[12]	Freund R W.A Transpoe-free quasi-minimal residual algorithm for non-Hermitian linear systems[J].Numer Maths,1992,14(2):470~482.
[13]	Parlett B N,Taylor D R,Liu Z A.A look-ahead Lanczos algorithm for unsymmetric matrices[J].Math Comp,1985,(44):105~124.
[14]	Freund R W,Nachtigal N M.QMR:a quasi-minimal residual methods for non-Hermitian linear systems[J].Numer Math,1991,(60):315~339.
[15]	Zhou L,Walker H F.Residual smoothing techniques for iterative methods[J].SIAM J Sci Comput,1994,15(2):297~312.
[16]	Van Der Worst H A.Bi-CGSTAB:a fast and smoothly convergence variant of Bi-CG for the solution of nonsymmetric linear systems[J].SIAM J Sci Comput,1992,13(2):631~644.
[17]	Chan T F,Gallopoulos E,Simoncini V,et al.A quasi-minimal residual variant of the Bi-SGSTAB algorithm for nonsymmetric systems[J].SIAM J Sci Comput,1994,15(2):338~347.
[18]	Ressel K J,Gutknecht M H.QMR smoothing for Lanczos-type product methods based on three-term recurrences[J].SIAM J Sci Comput,1998,19(1):55~73.
[19]	陈月明.油藏数值模拟基础[M].山东:石油大学出版社,1989.
[20]	胡家赣.线性代数方程组的迭代解法[M].北京:科学出版社,1991.
[21]	Saad Y.A flexible inner-outer preditioned GMRES algorithm[J].SIAM J Sci Comput,1993,14(2):461~469.
[22]	Kasenally E M.GMBACK:a generalised minimum backward error algorithm for nonsymmetric linear systems[J].SIAM J Sci Comput,1995,16(3):698~719.
[23]	Saunders M A,Simon H D,Yips E L.Two conjugate-gradient-type methods for unsymmetric linear equations[J].SIAM J Numer An al,1988,25(4):927~940.