地下水流动空间数据并行计算的研究
|
摘要
地下水资源的合理利用与水质监控是关系民生的大事。地下水流动系统的研究是实现地下水资源定量评价与预测的重要工具，为地下水资源的可持续利用提供了决定性支持。地下水流动规律反映的是地下水的水位随着时间与空间的变化规律，因此地下水流动系统研究的本质为地下水流动空间数据的研究。地下水流动系统研究的不断发展要求网格粒度日益精细以及研究尺度日渐扩大，庞大的数据计算量使得模拟时间过长而无法满足实际的需求。并行计算技术的出现为求解数据密集型的计算任务提供了一种非常有效的手段，因此，本文研究的目的在于借助并行计算技术实现地下水流动空间数据的快速且高效模拟。
本文研究的重点是地下水流动空间数据有限差分数值模型的并行模拟，即借助并行计算的相关理论以及地下水领域已有的并行研究成果，针对不同的并行计算平台，提出地下水流动空间数据的并行模拟策略。论文的主要创新之处有：
（1）基于分布式共享内存并行系统，提出了基于MPI/OpenMP混合编程模型的重叠型区域分解算法的并行模拟策略，即将一个大的地下水流动模拟问题划分为若干个小的子问题，并实现了进程与线程两层的并行粒度。基于该并行策略，网格规模为60×100×100的数值模型在SMP集群上具有4个子区域的并行模拟加速比可达到3.31。
（2）基于CPU-GPU异构环境并行系统，提出了基于GPU的地下水流动空间数据并行模拟策略，即利用GPU加速地下水流动空间数据模拟流程中的模型计算。在支持GPU通用计算的并行平台，对地下水流动空间数据基于OpenMP、基于MPI/OpenMP以及基于GPU三种并行策略的模拟性能进行测试。实验结果表明，地下水流动空间数据基于GPU的并行模拟具有最佳的并行性能。
（3）基于CPU-GPU异构环境并行系统，提出了基于线性求解器CUSP的MODFLOW并行策略，即利用求解器CUSP替代MODFLOW的迭代求解法。针对MODFLOW基于OpenMP与基于CUSP的两种并行策略，以TWRI_LARGE模型为例，将两种策略的并行性能进行比较。实验结果表明，基于CUSP并行的MODFLOW具有更好的并行性能。
Rational use and quality monitoring of the groundwater is a major event of people'slivelihood. Research on the groundwater flow system is an important tool to achieve quantitativeevaluation and the forecast of groundwater resources. It also provides decisive supports for thesustainable use of groundwater resources. The groundwater flow pattern reflects the hydraulicheads change with the time and space. Therefore, research on the groundwater flow system canbe attributed to study the groundwater flow spatial data. The continuous development of thegroundwater flow system requires grid granularity finer and study area larger. The traditionalsimulation of groundwater flow spatial data makes simulation time too long and can not meet theactual demands. Emergence of parallel computing technology provides a very effective means tosolve data-intensive computing tasks. Therefore, the purpose of this thesis is using parallelcomputing technology to achieve a fast and efficient simulation of groundwater flow spatial data.
This thesis focuses on the parallel finite difference numerical simulation of groundwaterflow spatial data. Based on the relevant theories and existing parallel research on groundwater,this thesis proposes appropriate parallel numerical simulation strategies of groundwater flowspatial data for different parallel computers. The main innovations of the thesis are as follows.
I. This thesis proposes a MPI/OpenMP hybrid programming model based on overlappingdomain decomposition algorithm to parallelize the simulation of groundwater flow spatial data.That means dividing a large-scale groundwater flow spatial data problem into several smallsub-problems. This parallel strategy achieves a two-level parallelism granularity includingprocess and thread. For a numerical model with grid size60×100×100, the experimental resultsyield a speedup of3.31for four sub-regions on a SMP cluster with two nodes.
II. This thesis proposes a GPU-based parallel simulation strategy of groundwater flowspatial data. That means solving the numerical model of the groundwater flow spatial data onGPU. On parallel platforms support GPU general-purpose computing, this paper compares theparallel performance of three parallel strategies which are groundwater flow spatial data basedon OpenMP, MPI/OpenMP and GPU. The experimental results yield that the GPU-based parallelstrategy has the best parallel performance.
III. This thesis proposes a parallel MODFLOW based on a linear solver CUSP. That meansusing linear solver CUSP instead of the iterative methods in MODFLOW. This thesis makes aperformance comparison between parallel MODFLOW based on OpenMP and parallelMODFLOW based on CUSP. For the TWRI_LARGE numerical model, the experimental resultsyield the maximum speedup of5.31for the OpenMP-based MODFLOW when the simulation isparallelized by eight threads. On a computer with one GPU, the experimental results yield thespeedup of10.6for the CUSP-based MODFLOW.
本文研究的重点是地下水流动空间数据有限差分数值模型的并行模拟，即借助并行计算的相关理论以及地下水领域已有的并行研究成果，针对不同的并行计算平台，提出地下水流动空间数据的并行模拟策略。论文的主要创新之处有：
（1）基于分布式共享内存并行系统，提出了基于MPI/OpenMP混合编程模型的重叠型区域分解算法的并行模拟策略，即将一个大的地下水流动模拟问题划分为若干个小的子问题，并实现了进程与线程两层的并行粒度。基于该并行策略，网格规模为60×100×100的数值模型在SMP集群上具有4个子区域的并行模拟加速比可达到3.31。
（2）基于CPU-GPU异构环境并行系统，提出了基于GPU的地下水流动空间数据并行模拟策略，即利用GPU加速地下水流动空间数据模拟流程中的模型计算。在支持GPU通用计算的并行平台，对地下水流动空间数据基于OpenMP、基于MPI/OpenMP以及基于GPU三种并行策略的模拟性能进行测试。实验结果表明，地下水流动空间数据基于GPU的并行模拟具有最佳的并行性能。
（3）基于CPU-GPU异构环境并行系统，提出了基于线性求解器CUSP的MODFLOW并行策略，即利用求解器CUSP替代MODFLOW的迭代求解法。针对MODFLOW基于OpenMP与基于CUSP的两种并行策略，以TWRI_LARGE模型为例，将两种策略的并行性能进行比较。实验结果表明，基于CUSP并行的MODFLOW具有更好的并行性能。
Rational use and quality monitoring of the groundwater is a major event of people'slivelihood. Research on the groundwater flow system is an important tool to achieve quantitativeevaluation and the forecast of groundwater resources. It also provides decisive supports for thesustainable use of groundwater resources. The groundwater flow pattern reflects the hydraulicheads change with the time and space. Therefore, research on the groundwater flow system canbe attributed to study the groundwater flow spatial data. The continuous development of thegroundwater flow system requires grid granularity finer and study area larger. The traditionalsimulation of groundwater flow spatial data makes simulation time too long and can not meet theactual demands. Emergence of parallel computing technology provides a very effective means tosolve data-intensive computing tasks. Therefore, the purpose of this thesis is using parallelcomputing technology to achieve a fast and efficient simulation of groundwater flow spatial data.
This thesis focuses on the parallel finite difference numerical simulation of groundwaterflow spatial data. Based on the relevant theories and existing parallel research on groundwater,this thesis proposes appropriate parallel numerical simulation strategies of groundwater flowspatial data for different parallel computers. The main innovations of the thesis are as follows.
I. This thesis proposes a MPI/OpenMP hybrid programming model based on overlappingdomain decomposition algorithm to parallelize the simulation of groundwater flow spatial data.That means dividing a large-scale groundwater flow spatial data problem into several smallsub-problems. This parallel strategy achieves a two-level parallelism granularity includingprocess and thread. For a numerical model with grid size60×100×100, the experimental resultsyield a speedup of3.31for four sub-regions on a SMP cluster with two nodes.
II. This thesis proposes a GPU-based parallel simulation strategy of groundwater flowspatial data. That means solving the numerical model of the groundwater flow spatial data onGPU. On parallel platforms support GPU general-purpose computing, this paper compares theparallel performance of three parallel strategies which are groundwater flow spatial data basedon OpenMP, MPI/OpenMP and GPU. The experimental results yield that the GPU-based parallelstrategy has the best parallel performance.
III. This thesis proposes a parallel MODFLOW based on a linear solver CUSP. That meansusing linear solver CUSP instead of the iterative methods in MODFLOW. This thesis makes aperformance comparison between parallel MODFLOW based on OpenMP and parallelMODFLOW based on CUSP. For the TWRI_LARGE numerical model, the experimental resultsyield the maximum speedup of5.31for the OpenMP-based MODFLOW when the simulation isparallelized by eight threads. On a computer with one GPU, the experimental results yield thespeedup of10.6for the CUSP-based MODFLOW.
引文
Ashby, S. F. and Falgout, R. D. A Parallel Multigrid Preconditioned Conjugate Gradient Algorithm forGroundwater Flow Simulations. Nuclear Science and Engineering,1995,124(1):145-159
Ashby, S. F., Bosl, W. J., Falgout, R. D., et al. A numerical simulation of groundwater flow and contaminanttransport on the Cray T3D and C90supercomputers. International Journal of High PerformanceComputing Applications,1999,13(1):80-93
Bandilla, K. W., Jankovic, I., Rabideau, A. J. A new algorithm for analytic element modeling of large-scalegroundwater flow. Advances in water resources,2007,30(3):446-454
Barrachina, S., Castillo, M., Igual, F. D., et al. Solving Dense Linear Systems on Graphics Processors. LectureNotes in Computer Science,2008
Barrett, R., Berry, M., Chan, F. T., et al. Templates for the solution of linear systems: building blocks foriterative methods, Society for Industrial Mathematics,1994
Barua, J. and Horne, R.N. Improving the performance of parallel(and series)reservoir simulation. InProceedings of Tenth SPE Symposium on Reservoir Simulation, Houston, TX, February6-8,1989:7-18
Bathe, K. J. and Wilson, E. Numerical methods in Finite Element Analysis. Prentice-Hall, Inc.,1976
Bell, N. and Garland, M. Efficient sparse matrix-vector multiplication on CUDA. NVIDIA Corporation,NVIDIA Technical Report NVR-2008-004,2008
Bell, N. and Garland, M. Implementing sparse matrix-vector multiplication on throughput-oriented processors.In:eds. Proceedings of the Conference on High Performance Computing Networking, Storage andAnalysis, ACM,2009,1-11
Berenguer, L., Dufaud, T., Tromeur-Dervout, D. Aitken’s acceleration of the Schwarz process using singularvalue decomposition for heterogeneous3D groundwater flow problems. Computers&Fluids,2013,80:320-326
Bhogeswara, R. and Killough, J. E. Parallel linear solvers for reservoir simulation: generic approach forexisting and emerging computer architectures. In Proceedings of12th SPE Symposium on ReservoirSimulation, New Orleans, LA,28February–March3,1993:71–82
Bolz, J., Farmer, I., Grinspun, E., et al. Sparse matrix solvers on the GPU: conjugate gradients and multigrid.ACM Transactions on Graphics (TOG)-Proceedings of ACM SIGGRAPH2003.2003,22(3):917-924
Briens, F. J. L., Wu, C. H., Gazdag, J., et al. Compositional reservoir simulation in parallel supercomputingenvironments. In Proceedings of Eleventh SPE Symposium on Reservoir Simulation, Anaheim, CA, Feb17–20,1991:125–133
Brodtkorb, A. R., Hagen, T. R., Saetra, M. L. Graphics processing unit (GPU) programming strategies andtrends in GPU computing. Journal of Parallel and Distributed Computing.2013,73(1):4-13
Chakib, A., Ellabib, A., Nachaoui, A. A domain decomposition convergence for elasticity equations.Mathematics and Computers in Simulation,2008,2:154-167
Chakroun I., Melab N., Mezmaz M., et al. Combining multi-core and GPU computing for solvingcombinatorial optimization problems. J.ParallelDistrib.Comput,2013,73:1563-1577
Cheng, T. P. and Wang, Q. Parallel Preconditioned Solver for Three-dimensional Groundwater Flow Equation.The2nd China-Japan Graduate Student Forum. Beijing,2009
Class, H., Helmig, R., Bastian, P. Numerical simulation of non-isothermal multiphase multicomponentprocesses in porous media.:1. An efficient solution technique. Advances in Water Resources,2002,25:533-550
Coats, K. H. Reservoir simulation. Petroleum Engineering Handbook. T. X. Richardson, Society of PetroleumEngineers:1-20
Coumou, D., Matthai, S., Geiger, S., et al. A parallel FE-FV scheme to solve fluid flow in complex geologicmedia. Computers&Geosciences,2008,34(12):1697-1707
CULA.2011. CULA-GPU Accelerated Linear Algebra. http://www.culatools.com/
Cusp.2011. Cusp-Generic parallel algorithms for sparse matrix and graph computations.http://code.google.com/p/cusp-library
cuSPARSE.2011. cuSPARSE-The NVIDIA CUDA Sparse Matrix Library.https://developer.nvidia.com/cusparse
Dawson, C. N., Klíe, H., Wheeler, M. F., et al. A parallel, implicit, cell centered method for two-phase flowwith a preconditioned Newton-Krylov solver. Computational Geosciences,1997,1(3):215-249
Dogru, A. H., Li, K. G., Sunaidi, H. A., et al. A massively parallel reservoir simulator for large scale reservoirsimulation. SPE Reservoir Simulation Symposium. Houston,1999
Dong, Y. H. and Li, G. M. A parallel PCG solver for MODFLOW. Ground Water,2009,47(6):845-850
Dongarra, J. J., Foster, I., Fox, G., et al. Sourcebook of parallel computing, Morgan Kaufmann Publishers,2003
Eppstein, M. J. and Dougherty, D. E. A comparative study of PVM workstation cluster implementations of atwo-phase subsurface flow model. Advances in water resources,1994,17(3):181-195
Georgescu, S. and Okuda, H. Conjugate gradients on multiple GPUs. International Journal for NumericalMethods in Fluids,2010,64(10):1254-1273
Goumas, G., Kourtis, K., Anastopoulos, N., et al. Performance evaluation of the sparse matrix-vectormultiplication on modem architectures. The Journal of Supercomputing,2009,50:36-77
Gwo, J. P., Eduardo, F. D., Hartmut, F., et al. HBGC123D: a high-performance computer model of coupledhydrogeological and biogeochemical processes. Computers&Geosciences,2001,27：1231-1242
Harbaugh, A. W., Banta, E. R., Hill, M. C. Mcdonald MG (2000) Modflow-2000, the U. S. Geological surveymodular groundwater model-user guide to modularization concepts and the ground-water flow process.US Geological Survey OpenFile Report0092
Hayes, E. F. Report of the Task Force of the Future of the NSF Supercomputer Centers Program,1995
He, K., Zheng, L., Dong, S., et al. PGO: A parallel computing platform for global optimization based ongenetic algorithm. Computers&geosciences,2007,33(3):357-366
He, Y. and Ding, C. H. Q. Mpi and openmp paradigms on cluster of smp architectures: the vacancy trackingalgorithm for multi-dimensional array transposition. In Proceedings of the2002ACM/IEEE conferenceon Supercomputing. IEEE Computer Society Press,2002
Hestenes, M. R. and Stiefel, E. Methods of conjugate gradients for solving linear systems. Journal of Researchof the National Bureau of Standards,1952,49(6):409-436
Herbst, M. and Gottschalk, S. On preconditioning for a parallel solution of the Richards equation. Computers&geosciences,2008,34(12):1958-1963
Hill, M. C., Geological, S. U. Preconditioned conjugate-gradient2(PCG2), a computer program for solvingground-water flow equations, Dept. of the Interior, US Geological Survey,1990
OpenMP. https://computing.llnl.gov/tutorials/openMP/#ProgrammingModel
Huang, J., Christ, J. A., Goltz, M. N. An Assembly Model for Simulation of Large-Scale Ground Water Flowand Transport. Ground Water,2008,46(6):882-892
Ian, J., Farmer, I., Grinspun, E., et al. Sparse matrix solvers on the gpu: conjugate gradients and multigrid.ACM Trans Graph,2003,22:917-924
Jacobsen, D. A., Julien, T. C., Inanc, S., et al. An MPI-CUDA implementation for massively parallelincompressible flow computations on multi-GPU clusters. In Proceedings of the48th AIAA AerospaceSciences Meeting and Exhibit. Orlando, Florida, the American Institute of Aeronautics and Astronautics,2010
Jeun, W. C., Kee, Y. S., Ha, S., et al. Overcoming performance bottlenecks in using OpenMP on SMP clusters.Parallel Computing,2008,34(10):570-592
Jiang, B. A parallel domain decomposition method for coupling of surface and groundwater flows. ComputerMethods in Applied Mechanics and Engineering,2009,198(9):947-957
Jin, H. Q., Jespersen, D., Mehrotra, P., et al. High performance computing using MPI and OpenMP onmulti-core parallel systems. Parallel Computing,2011,37:562–575
Jones, J. E. and Woodward, C. S. Newton-Krylov-multigrid solvers for large-scale, highly heterogeneous,variably saturated flow problems. Advances in Water Resources,2001,24(7):763-774
Keese, A. and Matthies, H. G. Parallel computation of stochastic groundwater flow. Proceedings of the NICSymposium2003.2003,20:399-408
Killough, J.and Commander, D. Scalable parallel reservoir simulation on a Windows NT-basedworkstation cluster. SPE symposium on reservoir simulation. Houston,1999
Konikow, L. F., Hornberger, G. Z., Halford, K. J., et al. Revised Multi-Node Well (MNW2) Package forMODFLOW Ground-Water Flow Model,2009
Kumbhar, P. Performance of PETSc GPU Implementation with Sparse Matrix Storage Schemes. MSc in HighPerformance Computing,2011
Kuznik, F., Obrecht, C., Rusaouen, G., et al. LBM based flow simulation using GPU computing processor.Computers and Mathematics with Applications,2010(59):2380-2392
Lanczos, C. Solution of systems of linear equations by minimized iterations. Journal of Research of theNational Bureau of Standards,1952,49(1):33-53
Lake L. W. Petroleum Engineering Handbook. Society of Petroleum Engineers,1997:1-20
Li Q., Salman R., Test E., et al. Parallel multi task cross validation for Support Vector Machine using GPU.Journal of Parallel Distributed Computing,2013,73:293-302
Mehl, S. W., Hill M. C., United, S. D., et al. MODFLOW-2000, the US Geological Survey ModularGround-water Model: User Guide to the Link-AMG (LMG) Package for Solving Matrix Equations Usingan Algebraic Multigrid Solver, US Dept. of the Interior. US Geological Survey,2001
Meijerink, J.A., Daalen, D.T., Hoogerbrugge, P. J., et al. Towards a more efficient parallel reservoir simulator.In Proceedings of Eleventh SPE Symposium on Reservoir Simulation, Anaheim, CA, February17–20,1991:107–116
Mirghani, B. Y., Mahinthakumar, K. G., Tryby, E. T., et al. A parallel evolutionary strategy basedsimulation–optimization approach for solving groundwater source identification problems. Advances inWater Resources,2009,32:1373-1385
Mustapha, H., Ghorayeb, A., Mustapha, K. A. Underground flow simulations using parallel finite elementmethod. Computers&Geosciences,2010,36(2):161-166
Nadeem, S. A. Parallel domain decomposition preconditioning for the adaptive finite element solution ofelliptic problems in three dimensions, Ph.D. dissertation, The University of Leeds School of Computing,2001.
Nakajima, K. Large-scale Simulations of3D Groundwater Flow using Parallel Geometric Multigrid Meth.Procedia Computer Science,2013,18:1265-1274
NVIDIA.2009. Nvidia CUDATM Programming Guide Version2.2
NVIDIA.2009. CUDA CUBLAS library version2.2
NVIDIA.2012. NVIDIA CUDATM Programming Guide Version5.0
Par s, J., Colominas, I., Navarrina, F., et al. Parallel computing in topology optimization of structures withstress constraints. Computers&Structures,2013,125:62-73
Pini, G. and Putti M. Parallel finite element laplace transform method for the non-equilibrium groundwatertransport equation. International journal for numerical methods in engineering,1997,40(14):2653-2664
Quandalle, P. and Moriano, S. Vectorization and parallel processing of models with local refinement. InProceedings of Eleventh SPE Symposium on Reservoir Simulation, Anaheim, CA, February17–20,1991:93–105
Raju, M. P. and Khaitan, S. Domain decomposition based high performance parallel computing. InternationalJournal of Computer Science Issuess,2009,9:27-32
Rinaldi, P. R., Dari, E. A., Vénere, M. J., et al. A Lattice–Boltzmann solver for3D fluid simulation on GPU.Simulation Modelling Practice and Theory,2012,25:163-171
Rybakin, B. P. Modeling of III-D problems of gas dynamics on multiprocessing computers and GPU.Computers&Fluids,2013,80:403-407
Saad, Y. Iterative methods for sparse linear systems. Society for Industrial Mathematics,2003
Saad, Y. and Schultz, M. H. GMRES: A generalized minimal residual algorithm for solving nonsymmetriclinear systems. SIAM Journal on Scientific and Statistical Computing,1986,7(3):856-869
Saied, F. Efficient Parallel Multigrid based Solvers for Large Scale Groundwater Flow Simulations.Computers&Mathematics with Applications,1998,35(7):45-54
Shewchuk, J. An introduction to conjugate gradient method without the agonizing pain. Technical reportCS-94-125. Carnegie Mellon University, Pittsburgh,1994.
Sikora, J. and Grzywacz, T. Domain decomposition method for diffuse optical tomography problems.Engineering Analysis with Boundary Elements,2012,2:1005-1013
Tang, G., D'Azevedo, E. F., Zhang, F., et al. Application of a hybrid MPI/OpenMP approach for parallelgroundwater model calibration using multi-core computers. Computers&Geosciences,2010,36(11):1451-1460
TOP500.2013. http://www.top500.org/list/2013/06/(accessed July26,2013).
Tsai, W. F., Shen, C. Y., Fu, H. H., et al. Study of Parallel Computation for Ground-Water Solute Transport.Journal of Hydrologic Engineering,1999,4:49-56
Tutkun, B. and Edis, F. O. A GPU application for high-order compact finite difference scheme. Comput&Fluids,2012,55:29-35
Vereecken, H., Neuendorf, O., Lindenmayr, G., et al. A Schwarz domain decomposition method for solutionof transient unsaturated water flow on parallel computers. Ecological modelling,1996,93(1-3):275-289
Verschoor, M., and Jalba, A.C. Analysis and performance estimation of the conjugate gradient method onmultiple GPUs. Parallel Computing,2012,38(10):552-575
Wang, P., Balay, S., Sepehrnoori, K., et al. A Fully Implicit Parallel EOS Compositional Simulator for LargeScale Reservoir Simulation. SPE15th Reservoir Simulation Symposium. Houston,1999
Wang, W. Q., Kosakowski, G., Kolditz, O. A parallel finite element scheme for thermo-hydro-mechanical(THM) coupled problems in porous media. Computers&Geosciences,2009,35:1631-1641
Watson, I. A., Crouch, R. S., Bastian, P., et al. Advantages of using adaptive remeshing and parallel processingfor modelling biodegradation in groundwater. Advances in Water Resources,2005,28:1143-1158
Wheeler, M. F., Arbogast, T., Bryant, S., et al. A parallel multiblock/multidomain approach for reservoirsimulation. Society of Petroleum Engineers,1999,2:14-17
Wilson, J. D. and Naff, R. L. The US Geological Survey modular ground-water model-GMG linear equationsolver package documentation. US Geological Survey Open-File Report,2004,1261:47
Wu, Y. S., Zhang, K., Ding, C., et al. An efficient parallel-computing method for modeling nonisothermalmultiphase flow and multicomponent transport in porous and fractured media. Advances in waterresources,2002,25(3):243-261
Yevi, G., Cinnella, P., Zhuang, X. On parallelizing a groundwater pollution simulator. Applied mathematicsand computation,1998,89(1-3):313-325
Yu, Z. B. Application of vector and parallel supercomputers to ground-water flow modeling. Computers&Geosciences,1997,23(9):917-927
Zhang, H., Schwartz, F. W., Sudicky, E. A. On the vectorization of finite element codes for high-performancecomputers. Water Resources Research,1994,30(12):3553-3559
Zhang, K., Wu, Y. S., Ding, C., et al. Application of parallel computing techniques to large-scale reservoirsimulation. Proceedings of the Twenty-Sixth Annual Workshop, Geothermal Reservoir Engineering.Stanford, CA (US).: Stanford University,2001a
Zhang, K., Wu, Y. S., Ding, C., et al. Parallel computing techniques for large-scale reservoir simulation ofmulti-component and multiphase fluid flow. SPE Reservoir Simulation Symposium,2001b
Zhang, K., Wu, Y. S., Bodvarsson, G. S. Parallel computing simulation of fluid flow in the unsaturated zone ofYucca Mountain, Nevada. Journal of contaminant hydrology,2003,62:381-399
Zhang, Q. F., Lan, S. Q., Wang, Y. M., et al. A new numerical method for groundwater flow and solutetransport using Velocity field. Journal of Hydrodynamics,2008,20(3):356-364
曹建文.大规模油藏数值模拟并行软件中的高效求解及预处理技术:[博士学位论文].北京:中国科学院软件所,2002
曹玉翡. MORTAR有限体积元方法及多孔介质中两相流的分相流动形式的研究:[博士学位论文].山东大学,2007
陈崇希,唐仲华.地下水流动问题数值方法,中国地质大学出版杜,1990
陈国良,安虹,陈崚,等.并行算法实践,高等教育出版社,2004
陈文光，武永卫等译. MPI与OpenMP并行程序设计.清华大学出版社，2004,10
程汤培，莫则尧，邵景力.基于JASMIN的地下水流大规模并行数值模拟.计算物理,2013,30(3):317~325
程汤培,王群,季晓慧,等.一种孔隙介质中地下水流并行计算方法.计算机工程与应用,2011,47(20):234~237
崔可锐.水文地质学基础,合肥工业大学出版社,2011
邓永辉.溶质运移模型数值解及并行化处理.辽东学院学报（自然科学版）,2010,17(4):337~341
丁皓江,何福保.弹性塑性力学中的有限单元法.北京:机械工业出版社,1989
丁继红,周德亮.国外地下水模拟软件的发展现状与趋势.勘察科学技术,2002(1):37~42
董艳辉,李国敏,郭永海等.应用并行PEST算法优化地下水模型参数.工程地质学报,2010,18(1):140~144
多核系列教材组编写组.多核程序设计.清华大学出版社,2007:159~165
多相复杂系统国家重点实验室多尺度离散模拟项目组.基于GPU的多尺度离散模拟并行计算.科学出版社,2009
都志辉.高性能计算之并行编程技术—MPI并行程序设计.清华大学出版社,2001,8
风辰（译）. CUDA编程指南4.0中文版,2009.4
郭卫星，卢国平，朱学愚，等. MODFLOW:模块化三维有限差分地下水流动模型.美国地质调查局水资源调查技术丛书之六.1999,6
郝治福,康绍忠.地下水系统数值模拟的研究现状和发展趋势[J].水利水电科技进展,2006.2(1):77~81
胡悦.并行计算时间与内存关系研究:[博士学位论文].上海大学,2011
黄林显,邵景力,崔亚莉,等.地下水数值模拟中P-PCG并行子程序包的改进.湖南科技大学学报(自然科学版),2012,27(2):83~87
黄林显,邵景力,崔亚莉,等.大区域地下水模拟的预优并行GMRES(m)算法研究.现代地质,2012,26(3):614~619
黄勇,周志芳.基于区域分解算法的地下水耦合模型及其应用.工程地质学报,2007,15(1):103~107
江春波,安晓谧.二维非恒定渗流的有限元并行计算.水科学进展,2004,15(4):454~457
江思珉,朱国荣,胡西嘉等.单纯形-模拟退火混合算法反求水文地质参数及其并行求解.地质评论,2007,53(1):92~97
孔祥龙,朱国荣,江思珉.应用改进并行遗传算法发求水文地质参数研究.高校地质学报,2008,14(1):126~132
李维山. MPI环境下TOUGHREACT并行化实现:[硕士学位论文].吉林大学,2012
李晓梅，吴建平. Krylov子空间方法及其并行计算.计算机科学,2005,32(1):19~20
李永瑾.基于本体的MPI+OpenMP并行检索研究与应用:[硕士学位论文].西北大学,2011
刘国东,丁晶.地下水动态并行预测方法.水文地质工程地质,1997(6):13~16
刘建霞.数值模型在青岛市大沽河水源地地下水水质预测中的应用:[硕士学位论文].中国海洋大学,2004
刘洋.二维热传导方程的并行计算与可视化研究:[硕士学位论文].天津师范大学,2004
刘耀炜.唐山7.8级地震地下水动力环境模拟研究:[博士学位论文].内蒙古农业大学,2008
鲁建霞,苟惠芳.有限元法的基本思想与发展过程.机械管理开发,2009,24(2):74~75
任国澄,朱国荣,江思珉. UCODE在反求水文地质参数中的应用及其并行求解.勘察科学技术,2010(3):7~11
孙峰根，等.水文地质计算的数值方法.中国矿业大学出版社,1995,6
王浩然,朱国荣,江思珉,等.基于区域分解法的地下水有限元并行数值模拟.南京大学学报:自然科学版,2005,41(3):245~252
王浩然,朱国荣,赵金熙.基于区域分解法的地下水有限元与边界元耦合模型.地质论评,2003,49(1):48~52
王惠春.基于SMP集群的MPI_OpenMP混合并行编程模型研究与应用:[硕士学位论文].湘潭大学,2008
王敏,魏久传,郭建斌等.区域分解算法在井田放水试验模拟中的应用.地下水,2010,32(1):1~3
王晓梅,于军,朱国荣,等.并行模拟技术在苏锡常地区地下水流模型建立中的应用.高效地质学报,2006,12(2):210~215
王仕琴,邵景力,宋献方,等.地下水模型MODFLOW和GIS在华北平原地下水资源评价中的应用.地理研究,2007,29(5):975~983
魏国孝,王德军,王刚,等. GIS技术和FEFLOW在酒泉东盆地地下水系统数值模拟中的应用.兰州大学学报(自然科学版),2007,43(6)
魏加华,李慈君,王光谦,等.地下水数值模型与组件GIS集成研究.吉林大学学报(地球科学版),2003,33(4):534~538
魏艳.基于LBM的两相流数值模拟及其并行算法的实现:[硕士学位论文].哈尔滨工业大学,2010
吴剑锋,彭伟,钱家忠等.基于INPG A的地下水污染治理多目标优化管理模型: II—实例应用.地质评论,2011,57(2):277~284
吴剑锋,彭伟,钱家忠等.基于INPG A的地下水污染治理多目标优化管理模型: II—实例应用.地质评论,2011,57(3):437~443
吴建平.稀疏线性代数方程组迭代法中的预处理技术研究:[博士学位论文].国防科技大学,2002
武强,朱斌,徐华,等. MODFLOW在淮北地下水数值模拟中的应用.辽宁工程技术大学学报,2005,24(4):500~503
徐腾.并行预处理共轭梯度法在内蒙能源基地地下水流场模型中的应用:[硕士学位论文].中国地质大学（北京）,2010
许向科.北京平原区地下水流动数值模拟研究:[硕士学位论文].中国地质大学（北京）,2006
徐小文.可扩展并行代数多重网格算法研究:[博士学位论文].北京:中国工程物理研究院,2007
姚平. CUDA平台上的CPU/GPU异步计算模式:[硕士学位论文].中国科学技术大学,2010
薛禹群,谢春红.水文地质学的数值法,煤炭工业出版社,1980
薛禹群,谢春红.地下水数值模拟.北京,科学出版社,2007
薛禹群,叶淑君,谢春红,等.多尺度有限元法在地下水模拟中的应用.水利学报,2004(7):1~8
杨多兴,李国敏,董艳辉,等．地下水流动三维有限差分模型并行计算．西南大学学报(自然科学版),2009,(10):149~153．
张二勇,李长青,李旭峰.区域地下水流数值模拟的方法和实践——以华北平原为例.中国地质,2009,36(4):920~926
张洪霞,宋文.地下水数值模拟的研究现状与展望.水利科技与经济.2007,13(11):794~796
张林波,迟学斌,莫则尧,等.并行计算导论.北京,清华大学出版社,2006
张奇.基于CUDA架构的MD5并行破解算法设计与实现:[硕士学位论文].电子科技大学,2012
张友良,冯夏庭,茹忠亮.基于区域分解算法的岩土大规模高性能并行有限元系统研究.岩石力学与工程学报,2004,23(21):3636~3641
周伟明.多核计算与程序设计.华中科技大学出版社,2009
Ashby, S. F., Bosl, W. J., Falgout, R. D., et al. A numerical simulation of groundwater flow and contaminanttransport on the Cray T3D and C90supercomputers. International Journal of High PerformanceComputing Applications,1999,13(1):80-93
Bandilla, K. W., Jankovic, I., Rabideau, A. J. A new algorithm for analytic element modeling of large-scalegroundwater flow. Advances in water resources,2007,30(3):446-454
Barrachina, S., Castillo, M., Igual, F. D., et al. Solving Dense Linear Systems on Graphics Processors. LectureNotes in Computer Science,2008
Barrett, R., Berry, M., Chan, F. T., et al. Templates for the solution of linear systems: building blocks foriterative methods, Society for Industrial Mathematics,1994
Barua, J. and Horne, R.N. Improving the performance of parallel(and series)reservoir simulation. InProceedings of Tenth SPE Symposium on Reservoir Simulation, Houston, TX, February6-8,1989:7-18
Bathe, K. J. and Wilson, E. Numerical methods in Finite Element Analysis. Prentice-Hall, Inc.,1976
Bell, N. and Garland, M. Efficient sparse matrix-vector multiplication on CUDA. NVIDIA Corporation,NVIDIA Technical Report NVR-2008-004,2008
Bell, N. and Garland, M. Implementing sparse matrix-vector multiplication on throughput-oriented processors.In:eds. Proceedings of the Conference on High Performance Computing Networking, Storage andAnalysis, ACM,2009,1-11
Berenguer, L., Dufaud, T., Tromeur-Dervout, D. Aitken’s acceleration of the Schwarz process using singularvalue decomposition for heterogeneous3D groundwater flow problems. Computers&Fluids,2013,80:320-326
Bhogeswara, R. and Killough, J. E. Parallel linear solvers for reservoir simulation: generic approach forexisting and emerging computer architectures. In Proceedings of12th SPE Symposium on ReservoirSimulation, New Orleans, LA,28February–March3,1993:71–82
Bolz, J., Farmer, I., Grinspun, E., et al. Sparse matrix solvers on the GPU: conjugate gradients and multigrid.ACM Transactions on Graphics (TOG)-Proceedings of ACM SIGGRAPH2003.2003,22(3):917-924
Briens, F. J. L., Wu, C. H., Gazdag, J., et al. Compositional reservoir simulation in parallel supercomputingenvironments. In Proceedings of Eleventh SPE Symposium on Reservoir Simulation, Anaheim, CA, Feb17–20,1991:125–133
Brodtkorb, A. R., Hagen, T. R., Saetra, M. L. Graphics processing unit (GPU) programming strategies andtrends in GPU computing. Journal of Parallel and Distributed Computing.2013,73(1):4-13
Chakib, A., Ellabib, A., Nachaoui, A. A domain decomposition convergence for elasticity equations.Mathematics and Computers in Simulation,2008,2:154-167
Chakroun I., Melab N., Mezmaz M., et al. Combining multi-core and GPU computing for solvingcombinatorial optimization problems. J.ParallelDistrib.Comput,2013,73:1563-1577
Cheng, T. P. and Wang, Q. Parallel Preconditioned Solver for Three-dimensional Groundwater Flow Equation.The2nd China-Japan Graduate Student Forum. Beijing,2009
Class, H., Helmig, R., Bastian, P. Numerical simulation of non-isothermal multiphase multicomponentprocesses in porous media.:1. An efficient solution technique. Advances in Water Resources,2002,25:533-550
Coats, K. H. Reservoir simulation. Petroleum Engineering Handbook. T. X. Richardson, Society of PetroleumEngineers:1-20
Coumou, D., Matthai, S., Geiger, S., et al. A parallel FE-FV scheme to solve fluid flow in complex geologicmedia. Computers&Geosciences,2008,34(12):1697-1707
CULA.2011. CULA-GPU Accelerated Linear Algebra. http://www.culatools.com/
Cusp.2011. Cusp-Generic parallel algorithms for sparse matrix and graph computations.http://code.google.com/p/cusp-library
cuSPARSE.2011. cuSPARSE-The NVIDIA CUDA Sparse Matrix Library.https://developer.nvidia.com/cusparse
Dawson, C. N., Klíe, H., Wheeler, M. F., et al. A parallel, implicit, cell centered method for two-phase flowwith a preconditioned Newton-Krylov solver. Computational Geosciences,1997,1(3):215-249
Dogru, A. H., Li, K. G., Sunaidi, H. A., et al. A massively parallel reservoir simulator for large scale reservoirsimulation. SPE Reservoir Simulation Symposium. Houston,1999
Dong, Y. H. and Li, G. M. A parallel PCG solver for MODFLOW. Ground Water,2009,47(6):845-850
Dongarra, J. J., Foster, I., Fox, G., et al. Sourcebook of parallel computing, Morgan Kaufmann Publishers,2003
Eppstein, M. J. and Dougherty, D. E. A comparative study of PVM workstation cluster implementations of atwo-phase subsurface flow model. Advances in water resources,1994,17(3):181-195
Georgescu, S. and Okuda, H. Conjugate gradients on multiple GPUs. International Journal for NumericalMethods in Fluids,2010,64(10):1254-1273
Goumas, G., Kourtis, K., Anastopoulos, N., et al. Performance evaluation of the sparse matrix-vectormultiplication on modem architectures. The Journal of Supercomputing,2009,50:36-77
Gwo, J. P., Eduardo, F. D., Hartmut, F., et al. HBGC123D: a high-performance computer model of coupledhydrogeological and biogeochemical processes. Computers&Geosciences,2001,27：1231-1242
Harbaugh, A. W., Banta, E. R., Hill, M. C. Mcdonald MG (2000) Modflow-2000, the U. S. Geological surveymodular groundwater model-user guide to modularization concepts and the ground-water flow process.US Geological Survey OpenFile Report0092
Hayes, E. F. Report of the Task Force of the Future of the NSF Supercomputer Centers Program,1995
He, K., Zheng, L., Dong, S., et al. PGO: A parallel computing platform for global optimization based ongenetic algorithm. Computers&geosciences,2007,33(3):357-366
He, Y. and Ding, C. H. Q. Mpi and openmp paradigms on cluster of smp architectures: the vacancy trackingalgorithm for multi-dimensional array transposition. In Proceedings of the2002ACM/IEEE conferenceon Supercomputing. IEEE Computer Society Press,2002
Hestenes, M. R. and Stiefel, E. Methods of conjugate gradients for solving linear systems. Journal of Researchof the National Bureau of Standards,1952,49(6):409-436
Herbst, M. and Gottschalk, S. On preconditioning for a parallel solution of the Richards equation. Computers&geosciences,2008,34(12):1958-1963
Hill, M. C., Geological, S. U. Preconditioned conjugate-gradient2(PCG2), a computer program for solvingground-water flow equations, Dept. of the Interior, US Geological Survey,1990
OpenMP. https://computing.llnl.gov/tutorials/openMP/#ProgrammingModel
Huang, J., Christ, J. A., Goltz, M. N. An Assembly Model for Simulation of Large-Scale Ground Water Flowand Transport. Ground Water,2008,46(6):882-892
Ian, J., Farmer, I., Grinspun, E., et al. Sparse matrix solvers on the gpu: conjugate gradients and multigrid.ACM Trans Graph,2003,22:917-924
Jacobsen, D. A., Julien, T. C., Inanc, S., et al. An MPI-CUDA implementation for massively parallelincompressible flow computations on multi-GPU clusters. In Proceedings of the48th AIAA AerospaceSciences Meeting and Exhibit. Orlando, Florida, the American Institute of Aeronautics and Astronautics,2010
Jeun, W. C., Kee, Y. S., Ha, S., et al. Overcoming performance bottlenecks in using OpenMP on SMP clusters.Parallel Computing,2008,34(10):570-592
Jiang, B. A parallel domain decomposition method for coupling of surface and groundwater flows. ComputerMethods in Applied Mechanics and Engineering,2009,198(9):947-957
Jin, H. Q., Jespersen, D., Mehrotra, P., et al. High performance computing using MPI and OpenMP onmulti-core parallel systems. Parallel Computing,2011,37:562–575
Jones, J. E. and Woodward, C. S. Newton-Krylov-multigrid solvers for large-scale, highly heterogeneous,variably saturated flow problems. Advances in Water Resources,2001,24(7):763-774
Keese, A. and Matthies, H. G. Parallel computation of stochastic groundwater flow. Proceedings of the NICSymposium2003.2003,20:399-408
Killough, J.and Commander, D. Scalable parallel reservoir simulation on a Windows NT
Konikow, L. F., Hornberger, G. Z., Halford, K. J., et al. Revised Multi-Node Well (MNW2) Package forMODFLOW Ground-Water Flow Model,2009
Kumbhar, P. Performance of PETSc GPU Implementation with Sparse Matrix Storage Schemes. MSc in HighPerformance Computing,2011
Kuznik, F., Obrecht, C., Rusaouen, G., et al. LBM based flow simulation using GPU computing processor.Computers and Mathematics with Applications,2010(59):2380-2392
Lanczos, C. Solution of systems of linear equations by minimized iterations. Journal of Research of theNational Bureau of Standards,1952,49(1):33-53
Lake L. W. Petroleum Engineering Handbook. Society of Petroleum Engineers,1997:1-20
Li Q., Salman R., Test E., et al. Parallel multi task cross validation for Support Vector Machine using GPU.Journal of Parallel Distributed Computing,2013,73:293-302
Mehl, S. W., Hill M. C., United, S. D., et al. MODFLOW-2000, the US Geological Survey ModularGround-water Model: User Guide to the Link-AMG (LMG) Package for Solving Matrix Equations Usingan Algebraic Multigrid Solver, US Dept. of the Interior. US Geological Survey,2001
Meijerink, J.A., Daalen, D.T., Hoogerbrugge, P. J., et al. Towards a more efficient parallel reservoir simulator.In Proceedings of Eleventh SPE Symposium on Reservoir Simulation, Anaheim, CA, February17–20,1991:107–116
Mirghani, B. Y., Mahinthakumar, K. G., Tryby, E. T., et al. A parallel evolutionary strategy basedsimulation–optimization approach for solving groundwater source identification problems. Advances inWater Resources,2009,32:1373-1385
Mustapha, H., Ghorayeb, A., Mustapha, K. A. Underground flow simulations using parallel finite elementmethod. Computers&Geosciences,2010,36(2):161-166
Nadeem, S. A. Parallel domain decomposition preconditioning for the adaptive finite element solution ofelliptic problems in three dimensions, Ph.D. dissertation, The University of Leeds School of Computing,2001.
Nakajima, K. Large-scale Simulations of3D Groundwater Flow using Parallel Geometric Multigrid Meth.Procedia Computer Science,2013,18:1265-1274
NVIDIA.2009. Nvidia CUDATM Programming Guide Version2.2
NVIDIA.2009. CUDA CUBLAS library version2.2
NVIDIA.2012. NVIDIA CUDATM Programming Guide Version5.0
Par s, J., Colominas, I., Navarrina, F., et al. Parallel computing in topology optimization of structures withstress constraints. Computers&Structures,2013,125:62-73
Pini, G. and Putti M. Parallel finite element laplace transform method for the non-equilibrium groundwatertransport equation. International journal for numerical methods in engineering,1997,40(14):2653-2664
Quandalle, P. and Moriano, S. Vectorization and parallel processing of models with local refinement. InProceedings of Eleventh SPE Symposium on Reservoir Simulation, Anaheim, CA, February17–20,1991:93–105
Raju, M. P. and Khaitan, S. Domain decomposition based high performance parallel computing. InternationalJournal of Computer Science Issuess,2009,9:27-32
Rinaldi, P. R., Dari, E. A., Vénere, M. J., et al. A Lattice–Boltzmann solver for3D fluid simulation on GPU.Simulation Modelling Practice and Theory,2012,25:163-171
Rybakin, B. P. Modeling of III-D problems of gas dynamics on multiprocessing computers and GPU.Computers&Fluids,2013,80:403-407
Saad, Y. Iterative methods for sparse linear systems. Society for Industrial Mathematics,2003
Saad, Y. and Schultz, M. H. GMRES: A generalized minimal residual algorithm for solving nonsymmetriclinear systems. SIAM Journal on Scientific and Statistical Computing,1986,7(3):856-869
Saied, F. Efficient Parallel Multigrid based Solvers for Large Scale Groundwater Flow Simulations.Computers&Mathematics with Applications,1998,35(7):45-54
Shewchuk, J. An introduction to conjugate gradient method without the agonizing pain. Technical reportCS-94-125. Carnegie Mellon University, Pittsburgh,1994.
Sikora, J. and Grzywacz, T. Domain decomposition method for diffuse optical tomography problems.Engineering Analysis with Boundary Elements,2012,2:1005-1013
Tang, G., D'Azevedo, E. F., Zhang, F., et al. Application of a hybrid MPI/OpenMP approach for parallelgroundwater model calibration using multi-core computers. Computers&Geosciences,2010,36(11):1451-1460
TOP500.2013. http://www.top500.org/list/2013/06/(accessed July26,2013).
Tsai, W. F., Shen, C. Y., Fu, H. H., et al. Study of Parallel Computation for Ground-Water Solute Transport.Journal of Hydrologic Engineering,1999,4:49-56
Tutkun, B. and Edis, F. O. A GPU application for high-order compact finite difference scheme. Comput&Fluids,2012,55:29-35
Vereecken, H., Neuendorf, O., Lindenmayr, G., et al. A Schwarz domain decomposition method for solutionof transient unsaturated water flow on parallel computers. Ecological modelling,1996,93(1-3):275-289
Verschoor, M., and Jalba, A.C. Analysis and performance estimation of the conjugate gradient method onmultiple GPUs. Parallel Computing,2012,38(10):552-575
Wang, P., Balay, S., Sepehrnoori, K., et al. A Fully Implicit Parallel EOS Compositional Simulator for LargeScale Reservoir Simulation. SPE15th Reservoir Simulation Symposium. Houston,1999
Wang, W. Q., Kosakowski, G., Kolditz, O. A parallel finite element scheme for thermo-hydro-mechanical(THM) coupled problems in porous media. Computers&Geosciences,2009,35:1631-1641
Watson, I. A., Crouch, R. S., Bastian, P., et al. Advantages of using adaptive remeshing and parallel processingfor modelling biodegradation in groundwater. Advances in Water Resources,2005,28:1143-1158
Wheeler, M. F., Arbogast, T., Bryant, S., et al. A parallel multiblock/multidomain approach for reservoirsimulation. Society of Petroleum Engineers,1999,2:14-17
Wilson, J. D. and Naff, R. L. The US Geological Survey modular ground-water model-GMG linear equationsolver package documentation. US Geological Survey Open-File Report,2004,1261:47
Wu, Y. S., Zhang, K., Ding, C., et al. An efficient parallel-computing method for modeling nonisothermalmultiphase flow and multicomponent transport in porous and fractured media. Advances in waterresources,2002,25(3):243-261
Yevi, G., Cinnella, P., Zhuang, X. On parallelizing a groundwater pollution simulator. Applied mathematicsand computation,1998,89(1-3):313-325
Yu, Z. B. Application of vector and parallel supercomputers to ground-water flow modeling. Computers&Geosciences,1997,23(9):917-927
Zhang, H., Schwartz, F. W., Sudicky, E. A. On the vectorization of finite element codes for high-performancecomputers. Water Resources Research,1994,30(12):3553-3559
Zhang, K., Wu, Y. S., Ding, C., et al. Application of parallel computing techniques to large-scale reservoirsimulation. Proceedings of the Twenty-Sixth Annual Workshop, Geothermal Reservoir Engineering.Stanford, CA (US).: Stanford University,2001a
Zhang, K., Wu, Y. S., Ding, C., et al. Parallel computing techniques for large-scale reservoir simulation ofmulti-component and multiphase fluid flow. SPE Reservoir Simulation Symposium,2001b
Zhang, K., Wu, Y. S., Bodvarsson, G. S. Parallel computing simulation of fluid flow in the unsaturated zone ofYucca Mountain, Nevada. Journal of contaminant hydrology,2003,62:381-399
Zhang, Q. F., Lan, S. Q., Wang, Y. M., et al. A new numerical method for groundwater flow and solutetransport using Velocity field. Journal of Hydrodynamics,2008,20(3):356-364
曹建文.大规模油藏数值模拟并行软件中的高效求解及预处理技术:[博士学位论文].北京:中国科学院软件所,2002
曹玉翡. MORTAR有限体积元方法及多孔介质中两相流的分相流动形式的研究:[博士学位论文].山东大学,2007
陈崇希,唐仲华.地下水流动问题数值方法,中国地质大学出版杜,1990
陈国良,安虹,陈崚,等.并行算法实践,高等教育出版社,2004
陈文光，武永卫等译. MPI与OpenMP并行程序设计.清华大学出版社，2004,10
程汤培，莫则尧，邵景力.基于JASMIN的地下水流大规模并行数值模拟.计算物理,2013,30(3):317~325
程汤培,王群,季晓慧,等.一种孔隙介质中地下水流并行计算方法.计算机工程与应用,2011,47(20):234~237
崔可锐.水文地质学基础,合肥工业大学出版社,2011
邓永辉.溶质运移模型数值解及并行化处理.辽东学院学报（自然科学版）,2010,17(4):337~341
丁皓江,何福保.弹性塑性力学中的有限单元法.北京:机械工业出版社,1989
丁继红,周德亮.国外地下水模拟软件的发展现状与趋势.勘察科学技术,2002(1):37~42
董艳辉,李国敏,郭永海等.应用并行PEST算法优化地下水模型参数.工程地质学报,2010,18(1):140~144
多核系列教材组编写组.多核程序设计.清华大学出版社,2007:159~165
多相复杂系统国家重点实验室多尺度离散模拟项目组.基于GPU的多尺度离散模拟并行计算.科学出版社,2009
都志辉.高性能计算之并行编程技术—MPI并行程序设计.清华大学出版社,2001,8
风辰（译）. CUDA编程指南4.0中文版,2009.4
郭卫星，卢国平，朱学愚，等. MODFLOW:模块化三维有限差分地下水流动模型.美国地质调查局水资源调查技术丛书之六.1999,6
郝治福,康绍忠.地下水系统数值模拟的研究现状和发展趋势[J].水利水电科技进展,2006.2(1):77~81
胡悦.并行计算时间与内存关系研究:[博士学位论文].上海大学,2011
黄林显,邵景力,崔亚莉,等.地下水数值模拟中P-PCG并行子程序包的改进.湖南科技大学学报(自然科学版),2012,27(2):83~87
黄林显,邵景力,崔亚莉,等.大区域地下水模拟的预优并行GMRES(m)算法研究.现代地质,2012,26(3):614~619
黄勇,周志芳.基于区域分解算法的地下水耦合模型及其应用.工程地质学报,2007,15(1):103~107
江春波,安晓谧.二维非恒定渗流的有限元并行计算.水科学进展,2004,15(4):454~457
江思珉,朱国荣,胡西嘉等.单纯形-模拟退火混合算法反求水文地质参数及其并行求解.地质评论,2007,53(1):92~97
孔祥龙,朱国荣,江思珉.应用改进并行遗传算法发求水文地质参数研究.高校地质学报,2008,14(1):126~132
李维山. MPI环境下TOUGHREACT并行化实现:[硕士学位论文].吉林大学,2012
李晓梅，吴建平. Krylov子空间方法及其并行计算.计算机科学,2005,32(1):19~20
李永瑾.基于本体的MPI+OpenMP并行检索研究与应用:[硕士学位论文].西北大学,2011
刘国东,丁晶.地下水动态并行预测方法.水文地质工程地质,1997(6):13~16
刘建霞.数值模型在青岛市大沽河水源地地下水水质预测中的应用:[硕士学位论文].中国海洋大学,2004
刘洋.二维热传导方程的并行计算与可视化研究:[硕士学位论文].天津师范大学,2004
刘耀炜.唐山7.8级地震地下水动力环境模拟研究:[博士学位论文].内蒙古农业大学,2008
鲁建霞,苟惠芳.有限元法的基本思想与发展过程.机械管理开发,2009,24(2):74~75
任国澄,朱国荣,江思珉. UCODE在反求水文地质参数中的应用及其并行求解.勘察科学技术,2010(3):7~11
孙峰根，等.水文地质计算的数值方法.中国矿业大学出版社,1995,6
王浩然,朱国荣,江思珉,等.基于区域分解法的地下水有限元并行数值模拟.南京大学学报:自然科学版,2005,41(3):245~252
王浩然,朱国荣,赵金熙.基于区域分解法的地下水有限元与边界元耦合模型.地质论评,2003,49(1):48~52
王惠春.基于SMP集群的MPI_OpenMP混合并行编程模型研究与应用:[硕士学位论文].湘潭大学,2008
王敏,魏久传,郭建斌等.区域分解算法在井田放水试验模拟中的应用.地下水,2010,32(1):1~3
王晓梅,于军,朱国荣,等.并行模拟技术在苏锡常地区地下水流模型建立中的应用.高效地质学报,2006,12(2):210~215
王仕琴,邵景力,宋献方,等.地下水模型MODFLOW和GIS在华北平原地下水资源评价中的应用.地理研究,2007,29(5):975~983
魏国孝,王德军,王刚,等. GIS技术和FEFLOW在酒泉东盆地地下水系统数值模拟中的应用.兰州大学学报(自然科学版),2007,43(6)
魏加华,李慈君,王光谦,等.地下水数值模型与组件GIS集成研究.吉林大学学报(地球科学版),2003,33(4):534~538
魏艳.基于LBM的两相流数值模拟及其并行算法的实现:[硕士学位论文].哈尔滨工业大学,2010
吴剑锋,彭伟,钱家忠等.基于INPG A的地下水污染治理多目标优化管理模型: II—实例应用.地质评论,2011,57(2):277~284
吴剑锋,彭伟,钱家忠等.基于INPG A的地下水污染治理多目标优化管理模型: II—实例应用.地质评论,2011,57(3):437~443
吴建平.稀疏线性代数方程组迭代法中的预处理技术研究:[博士学位论文].国防科技大学,2002
武强,朱斌,徐华,等. MODFLOW在淮北地下水数值模拟中的应用.辽宁工程技术大学学报,2005,24(4):500~503
徐腾.并行预处理共轭梯度法在内蒙能源基地地下水流场模型中的应用:[硕士学位论文].中国地质大学（北京）,2010
许向科.北京平原区地下水流动数值模拟研究:[硕士学位论文].中国地质大学（北京）,2006
徐小文.可扩展并行代数多重网格算法研究:[博士学位论文].北京:中国工程物理研究院,2007
姚平. CUDA平台上的CPU/GPU异步计算模式:[硕士学位论文].中国科学技术大学,2010
薛禹群,谢春红.水文地质学的数值法,煤炭工业出版社,1980
薛禹群,谢春红.地下水数值模拟.北京,科学出版社,2007
薛禹群,叶淑君,谢春红,等.多尺度有限元法在地下水模拟中的应用.水利学报,2004(7):1~8
杨多兴,李国敏,董艳辉,等．地下水流动三维有限差分模型并行计算．西南大学学报(自然科学版),2009,(10):149~153．
张二勇,李长青,李旭峰.区域地下水流数值模拟的方法和实践——以华北平原为例.中国地质,2009,36(4):920~926
张洪霞,宋文.地下水数值模拟的研究现状与展望.水利科技与经济.2007,13(11):794~796
张林波,迟学斌,莫则尧,等.并行计算导论.北京,清华大学出版社,2006
张奇.基于CUDA架构的MD5并行破解算法设计与实现:[硕士学位论文].电子科技大学,2012
张友良,冯夏庭,茹忠亮.基于区域分解算法的岩土大规模高性能并行有限元系统研究.岩石力学与工程学报,2004,23(21):3636~3641
周伟明.多核计算与程序设计.华中科技大学出版社,2009