区域分解预处理器研究及其在地下水模拟中的应用*

南京大学学报(自然科学版) ›› 2012, Vol. 48 ›› Issue (6): 753–760.

区域分解预处理器研究及其在地下水模拟中的应用*

王佩¹，朱国荣¹**，江思氓²，孙斌堂³

出版日期:2015-09-10 发布日期:2015-09-10
作者简介: (1.南京大学水科学系，南京，210093;2.同济大学水利工程系，上海，200092
3.中国冶金地质工程勘察总局山东局，济南，250014
基金资助:
国家自然科学基金(41002078)

Domain decomposition preprocessor research and
its application in groundwater modeling

Wang Pei1，Zhu Uuo-Rong1 ,Jung Si-Min2，Sun Bin-Tang3

Online:2015-09-10 Published:2015-09-10
About author: (1 .Department of Hydrosciences,Nanjing University,Nanjing,210093,China;2. Department of Hydraulic
Engineering,Tongji University,Shanghai,200092,China;3. Shandong Bureau of
China Exploration and Engineering Bureau,Jinan,250014,China)

摘要/Abstract

摘要： 地下水数值计算中，如何提高大型稀疏线性代数方程组的求解效率一直备受关注.条件预处
理共辆梯度方法是求解大型稀疏线性代数方程组的有效方法，而如何构造高效的预处理器至关重要.木
文基于有限元理论介绍了区域分解预处理器（domain decomposition preprocessor,DDP)的设计原理及
实现过程，将其与预处理共辆梯度法结合为区域分解预处理共辆梯度法(DDP-PCG)并应用于地下水模
拟中.文中首先采用具有解析解的均质稳定流模型验证了DDP-PCG的可靠性;接着对该模型研究区进
行不同规模网格剖分，均采用CG, Jacobi-PCG, SSOR-PCG, DDP-PCG求解，结果表明DDP-PCG迭代收
敛次数几乎不随网格规模发生变化，具有很强的鲁棒性;随着网格规模的增加，DDP-PCG求解效率优势
更加显著.最后针对承压含水层介质参数连续变化和突变两种非均质问题，对研究区进行大规模网格剖
分，进一步证明在相同误差限下，DDP-PCG的求解效率高于其它三种方法.

Abstract: The problem that how to improve the efficiency of solving the large sparse linear algebraic equations has
always been of concern in groundwater numerical simulation. Preconditioned conjugate gradient method is an effective
method for solving large sparse linear algebraic equations. And how to construct efficient preprocessor is essential.
The domain decomposition preprocessor design principles and implementation process are descirbed based on the ti-
nite clement theory.The preconditioned conjugate gradient method with domain decomposition preconditioner(DDP-
PCU)is proposed and applied to groundwater simulation. Firstly, DDP-PCU’s reliability is proved with analytical
homogeneous model. Then CU,Jacobi-PCU,SSOR-PCU,DDP-PCU are used to solve the model under different subdi-
visions，which show that DDP-PCU is of strong robustness and the higher the subdivision is, the more notable is
DDP-PCG’s efficiency. Finally, inhomogencous confined aquifer with continuous coefficients and abrupt coefficients
are caculated under finely subdivision,which further prove that under the same error limit，DDP-PCU’s efficiency are
the highest of all.

王佩¹，朱国荣¹**，江思氓²，孙斌堂³. 区域分解预处理器研究及其在地下水模拟中的应用*[J]. 南京大学学报(自然科学版), 2012, 48(6): 753–760.

Wang Pei1，Zhu Uuo-Rong1 ,Jung Si-Min2，Sun Bin-Tang3. Domain decomposition preprocessor research and
its application in groundwater modeling
[J]. Journal of Nanjing University(Natural Sciences), 2012, 48(6): 753–760.

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