KRYLOV SUBSPACE PROJECTION METHOD AND ITS APPLICATION ON OIL RESERVOIR SIMULATION

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (6): 607-616.

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KRYLOV SUBSPACE PROJECTION METHOD AND ITS APPLICATION ON OIL RESERVOIR SIMULATION

刘晓明, 卢志明, 刘宇陆

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

收稿日期:1999-03-15 修回日期:1999-12-10 出版日期:2000-06-18 发布日期:2000-06-18
基金资助:
the National Natural Science Foundation of China(19872043)

KRYLOV SUBSPACE PROJECTION METHOD AND ITS APPLICATION ON OIL RESERVOIR SIMULATION

Liu Xiaoming, Lu Zhiming, Liu Yulu

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

Received:1999-03-15 Revised:1999-12-10 Online:2000-06-18 Published:2000-06-18
Supported by:
the National Natural Science Foundation of China(19872043)

摘要/Abstract

摘要： 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-Elimination 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 further presented.

关键词: Krylov subspace methods, block PE method, numerical oil reservoir simulation

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-Elimination 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 further presented.

Key words: Krylov subspace methods, block PE method, numerical oil reservoir simulation

中图分类号:

O241.6

刘晓明;卢志明;刘宇陆. KRYLOV SUBSPACE PROJECTION METHOD AND ITS APPLICATION ON OIL RESERVOIR SIMULATION[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(6): 607-616.

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.

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KRYLOV SUBSPACE PROJECTION METHOD AND ITS APPLICATION ON OIL RESERVOIR SIMULATION

KRYLOV SUBSPACE PROJECTION METHOD AND ITS APPLICATION ON OIL RESERVOIR SIMULATION

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