基于协同异构模型的成形模拟计算加速
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
成形模拟中的多场耦合分析,非线性多尺度耦合分析等问题通常需要对大量数据进行多次计算以得到有效的结果,另外这些计算又必须在合理的时间内完成。本文主要从并行计算架构方面研究成形模拟中的计算加速方法,提出了基于CPU/GPU架构的协同异构计算模型来缩短成形模拟过程中的计算时间。
     本文把工作重点放在了如何优化CPU/GPU协同异构计算模型,缩短计算时间问题的研究上,通过对成形模拟中求解多物理场耦合,多尺度耦合分析过程中的温度场问题,应力应变问题经常用到的有限差分法,矩阵与向量乘积等常用计算方法的GPU架构的程序实现,极大的提高了计算效率,将大量计算转移到计算效率较高的GPU架构上来,减轻CPU的计算压力,缩短计算时间。本文通过对六个数据存储优化方案的实验分析,不断优化CPU/GPU异构计算架构的设计方法,经过各种实验数据证明,得出了比较合适的数据存储方案,针对GPU架构在科学计算方面的一些缺陷,通过CPU来协同完成。通过将完全位串链表与位掩码结合在一起使用优化了存储器结构对计算性能的影响,测试发现,优化方案比没有优化过的方案有25倍的性能提升。在程序设计和收敛求和计算过程中充分利用共享内存空间,减少不必要的数据同步,减少导致缓存命中率下降的因素。通过使用分支同步的方法来处理条件分支,在发生条件分支时,转移方向相同线程的先执行完分支中的指令,然后另外一个转移方向的线程再执行另外一个分支中的指令优化了单指令多线程技术对计算性能的影响。
     通过实验评估,CPU/GPU协同异构计算模型能解决比单个CPU或者GPU计算系统大16倍左右的问题,却能得到少于20%的错误率,系统负载率只有之前的60%,系统计算效率有50%以上的提升。通过实验结果和并行计算系统现在的发展趋势,相信CPU/GPU协同异构计算将成为并行计算发展历程中越来越重要的一环。本文的研究内容具有重要的工程意义和广阔的应用前景。
Multi-physics coupling, nonlinear multi-scale coupling and other factors make large amounts of data need to be calculated in forming simulation,while these jobs must also be completed within a reasonable time.This thesis mainly focus on the research of parallel computing architecture accelerate computing for forming simulation, proposed collaborative heterogeneous computing model to shorten forming simulation computing time based on CPU/GPU architecture.
     In this thesis focus on how to optimize the CPU/GPU collaborative heterogeneous computing model and reduce the computing time. Some algorithm such as finite difference method, matrix and vector product are often used in calculating stress filed and temperature filed,which considered multi-physics coupling and multi-scale coupling. Those algorithms have been implemented under GPU architecture. Large calculation jobs are transferred to GPU architecture,which has a higher calculation efficiency, alleviate CPU calculation pressure and shorten computing time.Greatly improves calculation efficiency.Optimize CPU/GPU collaborative heterogeneous computing model design based on six experiments of data storage optimization analysis.A variety of experiment data show that had obtained better data storage solution.There are many shortcomings in GPU architecture for scientific computing, so must be coordinated by CPU to complete.Optimize data storage architecture on the computational performance of model through bit string array used together with bitmask.Test found no optimized program can be as high as 25 times compared to the optimized one.Make good use of shared memory,reduce unnecessary data synchronization,reduce cache hit rate of decline factors through program design and convergence calculation process. Synchronized by using the branch method to deal with conditional branches, conditional branches in the same direction, the transfer of the same thread of the first implementation of the direction of branch instructions completed, and then switch to the direction of another thread and then another branch of the implementation of optimized SIMT instructions threading the calculation of performance.
     With CPU/GPU collaborative and heterogeneous computing prototype shows that the performance model can predict the execution time of problem sizes that are 16 times as large as the profile runs with less than 20% error, and that the predicted optimal load distribution ratios have less than 60% and the resulting performance improvement using both CPUs and GPUs can be as high as 50% compared to using either a CPU core or a GPU.Based on our results and current trends in microarchitecture,Efficient use of CPU and GPU collaborative and heterogeneous computing environment will become increasingly important to high performance computing. The study in this paper is of great significance and wide application prospect.
引文
[1]毕文权.汽车桥壳热冲压成形工艺数值模拟及工程应用研究:[博士学位论文].材料学院,吉林大学,2009.
    [2]Jun Li,Jian Li,etc.Nonlinear identification of a DIR-SOFC stack using wavelet networks. Journal of Power Sources,2008,179:673-682.
    [3]http://www.nvidia.com/object/gpu.html
    [4]Kruger J,Westermann R.Acceleration Techniques for GPU-Based Volume Rendering.IEEE visualization,2003:678-683.
    [5]Gregory S J,Juhyun L,Christopher A B,etc.The Irregular Z-Buffer:Hardware Acceleration for Irregular Data Structure.ACM Transactions on Graphics,2005,24(4):1462-1482.
    [6]Telea A,Van Wijk. J.J.3D IBFV:Hardware-Accelerated 3D Flow Visualization.IEEE Visualization,2003,VIS 2003:798-803.
    [7]Botchen R P,Weiskopf D,Ertl T.Texture-Based Visualization of Uncertainty in Flow Fields.IEEE Visualization 2005 Proceedings,2005:647-654.
    [8]Govindaraju N K,Lin M C,Manocha D.Quick-CULLIDE:Efficient inter and intra object collision culling using graphics hardware.In Proceedings of IEEE Virtual Reality,2005:59-66.
    [9]Kruger J,Kipfer P,Kondratieva P,etc. A particle system for interactive visualization of 3D flows.IEEE Transaction on Visualization and Computer Graphics,2005,11(6):7 44-756.
    [10]Govindaraju N.K,Raghuvanshi N,Manocha D.Fast and approximate stream mining of quantiles and frequencies using graphics processors.In Proceedings of 2005 ACM SIGMOD International Conference on Management of Data,2005:611-622.
    [11]Meurant G.A review on the inverse of symmetric tridiagonal and block tridiagonal matrices. SIAM Journal on Matrix Analysis and Applications,1992,13:707.
    [12]柳有权.基于物理的计算机动画及其加速技术的研究:[博士学位论文].北京:中国科学院软件研究所.2005.
    [13]张怡,张加万,孙济洲等.基于可编程图形加速硬件的实时光线投射算法.系统仿真学报,2007,19(18):4204-4208.
    [14]刘保权,刘学慧,吴恩华.基于GPU的实时深度图像向前映射绘制算法.软件学报,2007,18(6):1531-1542.
    [15]汤颖,张宏鑫,张美玉.基于图形硬件的纹理图像编码与实时绘制算法.计算机学报,2007,30(2):272-280.
    [16]储璄骏,杨新,高艳.使用GPU编程的光线投射体绘制算法.计算机辅助设计与图形学学报,2007,19(2):257-262.
    [17]罗军,王玲.基于GPU的粒子系统的实现技术.微计算机信息,2008,24(2-1):273-275.
    [18]李建明,刘志轩,迟忠先等.基于生物模型和GPU加速的实时鱼类运动仿真.系统仿真学报,2007,19(16):3838-3842.
    [19]杨柏林,潘志庚.面向移动设备的各向异性纹理映射方法.计算机辅助设计与图形学学报,2007,19(5):569-574.
    [20]曹峰,周傲英.基于图形处理器的数据流快速聚类.软件学报,2007,18(2):291-301.
    [21]John D Owens,David Luebke,Nage Govindaraju,Mark Harris.A Survey of General-Purpose Computation on Graphics Hardware.EUROGRAPHICS 2005: 21-51.
    [22]Groche P,Kloepsch C. Sheet metal forming processes at elevated temperatures. Journal of Advanced Manufacturing Systems,2008,7(2):307-311.
    [23]Karl E H,Sergey M,Radek G.Nonlinear Optimization Framework for Image-Based Modeling on Programmable Graphics Hardware.ACM Transactions on Graphics,2003,22(3):925-934.
    [24]Ian Buck, Tim Foley,Daniel Horn,Jeremy Sugerman.Brook for GPUS,GCafe December 10th,2003:108-120.
    [25]http://graphics.stanford.edu/projects/brookgpu/lang.html.
    [26]NVIDIA CUDA Compute Unified Device Architecture Programming Guide.Version 1.0 2007.
    [27]http://www.nvidia.com.
    [28]http://www.dcc.uchile.cl/-gnavarro/software/
    [29]孟祥萍,钱进,冯雷,郑文,张维俊.基于位串数组的关联规则挖掘算法.计算机工程与应用,2004,18(2):291-301.
    [30]刘兴龙,曲仕尧.冲击碰撞中接触问题的数值模拟研究.山东机械,2005:14-17.
    [31]冯兰,蔡英文,何丹农,余震.金属板料成形数值模拟的研究现状.塑性工程学报,2004,(06):1-6.
    [32]崔振山,刘才.金属热成形过程的综合数值模拟.工程力学,2002,19(1):42-46.
    [33]陈劫实,周贤宾.板料成形极限的理论预测与数值模拟研究.塑性工程学报,2004,11(01):13-17.
    [34]Zimniak, Z Piela.A Finite element analysis of a tailored blanks stamping process. Journal of Materials Processing Technology.2000,106(1-3):254-260.
    [35]Zimniak, Z. Implementation of the forming limit stress diagram in FEM simulations. Journal of Materials Processing Technology.2000,106(1-3):261-266.
    [36]Xing W, Bao J, Yang Y. Numerical simulation of hot stamping of quenchable boron steel. Materials Science and Engineering,2009,499(1-2):28-31.
    [37]Wang H, Li E, Li G. Y. The least square support vector regression coupled with parallel sampling scheme metamodeling technique and application in sheet forming optimization. Materials & Design,2009,30(5):1468-1479.
    [38]Turetta A, Bruschi S, Ghiotti A Investigation of 22MnB5 formability in hot stamping operations. Journal of Materials Processing Technology,2006,177(1-3):395-400.
    [39]Santos A D, Teixeira P. A study on experimental benchmarks and simulation results in sheet metal forming. Journal of Materials Processing Technology,2008,199(1-3): 327-336.
    [40]Peng L, Hu P, Lai X, Mei D, etc. Investigation of micro/meso sheet soft punch stamping process-simulation and experiments. Materials & Design,2009,30(3): 783-790.
    [41]Naderi M., Uthaisangsuk V, Prahl U, Bleck W. A numerical and experimental investigation into hot stamping of boron alloyed heat treated steels. Steel Research International,2008,79(2):77-84.
    [42]Mori K, Maki S, Tanaka Y. Warm and hot stamping of ultra high tensile strength steel sheets using resistance heating. CIRP Annals-Manufacturing Technology,2005, 54(1):209-212.
    [43]Mori K, Ito D. Prevention of oxidation in hot stamping of quenchable steel sheet by oxidation preventive oil. CIRP Annals-Manufacturing Technology,2009,58(1): 267-270.
    [44]Merklein M, Lechler J, Geiger M. Characterisation of the Flow Properties of the Quenchenable Ultra High Strength Steel 22MnB5. CIRP Annals-Manufacturing Technology,2006,55(1):229-232.
    [45]Merklein M, Lechler J. Investigation of the thermo-mechanical properties of hot stamping steels. Journal of Materials Processing Technology,2006,177(1-3): 452-455.
    [46]Lin J, Dean T. A Modelling of microstructure evolution in hot forming using unified constitutive equations. Journal of Materials Processing Technology,2005,167(2-3): 354-362.
    [47]Lee D C, Han C S. CAE (computer aided engineering) driven durability model verification for the automotive structure development. Finite Elements in Analysis and Design,2009,45(5):324-332.
    [48]Hoffmann H, So H, Steinbeiss H. Design of Hot Stamping Tools with Cooling System. CIRP Annals-Manufacturing Technology,2007,56(1):269-272.
    [49]Groche P, Kloepsch C. Sheet metal forming processes at elevated temperatures. Journal of Advanced Manufacturing Systems,2008,7(2):307-311.
    [50]Grass H, Krempaszky C, Werner E.3-D FEM-simulation of hot forming processes for the production of a connecting rod. Computational Materials Science,2006,36(4): 480-489.
    [51]Firat M. Computer aided analysis and design of sheet metal forming processes:Part I-The finite element modeling concepts. Materials and Design,2007,28(4): 1298-1303.
    [52]Firat M. Computer aided analysis and design of sheet metal forming processes:Part Ⅲ:Stamping die-face design. Materials and Design,2007,28(4):1311-1320.
    [53]Chenot J L, Massoni E. Finite element modelling and control of new metal forming processes. International Journal of Machine Tools and Manufacture,2006,46(11 SPEC. ISS.):1194-1200.
    [54]Bontcheva N, Petzov G. Microstructure evolution during metal forming processes. Computational Materials Science,2003,28(3-4):563-573.
    [55]Bigot D, Roelandt J M, Kebir H. Numerical method coupling finite elements and boundary elements to model forming process tools. Journal of Materials Processing Technology,2009,209(7):3225-3235.
    [56]Bardelcik A, Salisbury C P, Winkler S, Wells M A, etc. Effect of cooling rate on the high strain rate properties of boron steel. International Journal of Impact Engineering, 37(6):694-702.
    [57]Assempour A,Hashemi R,Abrinia K,Ganjiani M,etc. A methodology for prediction of forming limit stress diagrams considering the strain path effect. Computational Materials Science,2009,45(2):195-204.
    [58]Min Li, Yi-sheng Zhang,etc.,An Authentication Service for Collaborative Manufacturing, ICCSIT 2008,Singapore August 29-September 2,2008:411-414.
    [59]李敏,张宜生,等.用于并行计算的PC集群系统构建.计算机应用研究,2009(2):1042-1043,1062.
    [60]闫欢,张宜生,梁书云等.基于规则引擎的制造企业MES系统原型研究[J].计算机工程,2007.33(7):210-212,214.
    [61]Li min,Zhang yisheng, Li Dequn,HPC Cluster Monitoring System Architecture Design and Implement,IEEE ICICTA09,2009,10.10-11:325-327.
    [62]Fan Z, Lin B, Costa F, et al. Three-dimensional warpage simulation for injection molding. Society of Plastics Engineers; 2004:491-495.
    [63]Koscher E, Fulchiron R. Influence of shear on polypropylene crystallization: morphology development and kinetics. Polymer,2002,43(25):6931-6942.
    [64]Pantani R, Coccorullo I, Speranza V, et al. Modeling of morphology evolution in the injection molding process of thermoplastic polymers. Progress in Polymer Science, 2005,30(12):1185-1222.
    [65]Han S, Wang KK. Use of the fast-cool pVT data for shrinkage analysis in injection molding. International Polymer Processing(Germany),2002,17(1):67-75.
    [66]Costa F, Fan Z, Kennedy P, et al. Three-Dimensional Cooling and Warpage Simulation for the Injection Over-Molding Process. Plastics Eng Annual Technical Conference (ANTEC); 2005:146.
    [67]Turng LS, Wang VW, Wang KK. Numerical Simulation of the Coinjection Molding Process. Journal of Engineering Materials and Technology,1993:115-148.
    [68]Cui S, Huang Z, Zhang Y. System Design and Implementation of an Integrated CAE System for Injection Molding. Polymer-Plastics Technology and Engineering,2008, 47(5):458-465.
    [69]Zhang yisheng, Li min, Li Dequn,Wireless Communication Management Model of Workshop and Warehouse Manufacturing System.IEEE ICICTA09,2009,10.10-11:121-123.
    [70]Hua-min Z, Zhang Y, De-qun LI. An improved injection molding filling simulation for 3D surface model. Journal of Basic Science and Engineering,2001,9(1):52-59.
    [71]Li Min, Zhang Yisheng,Job Monitoring Analysis Tool for HPC Clusters, IEEE iCISE2009,2009:262-264.
    [72]Zhang Yisheng, Li Min, Minimum Interference Model in Wireless Sensor Network for Foul Environment in Workshop and Warehouse, IEEE iCISE2009, 2009:183-185.
    [73]Li D, Zhou H. Modelling and simulation of residual stress and warpage in injection moulding. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,2004,218(5):521-30.
    [74]Zhou H, Xi GD, Li D. Modeling and simulation of shrinkage during the picture tube panel forming process. Journal of Manufacturing Science and Engineering,2007, 129:380.
    [75]Zhiqiang Zhang,Zhongchao Ye,Yisheng Zhang,Jian Li,Numerical Analysis on Hot Stamping of B Pillar Reinforcement of Automobiles,Advanced Materials Research,Vols.97-101 (2010) 282-285.
    [76]Chen L, Li J, Zhou H, et al. A study on gas-assisted injection molding filling simulation based on surface model of a contained circle channel part. Journal of Materials Processing Tech,2008,208(1-3):90-98.
    [77]莫健华,张宜生,吕言,张李超,大型机械多连杆式伺服压力机的性能与生产应用,MECT锻压装备与制造技术,2009(11):35-38.
    [78]程念胜,张宜生,等,一种基于令牌的单点登录认证服务,计算机应用,2008,28(12):53-55.
    [79]陈宇宏,张宜生,等,基于光学畸变要求的注射成型透明平板应力翘曲分析,航空材料学报,2008,128(6):37-43.
    [80]Cheng Niansheng, Zhang Yisheng,etc. Intranet Based Security Infrastructure for Manufacturing Grid, Genetic and Evolutionary Computing,2008. WGEC '08. Second International Conference,2008:247-250.
    [81]Yang WH, Peng A, Liu L, et al. Parallel true 3D CAE with hybrid meshing flexibity for injection molding.2005:55-60.
    [82]Fan Z, Zheng R, Kennedy P, etc. Warpage Analysis of Solid Geometry.2000: 2008-2010.
    [83]Gropp W, Lusk E, Doss N, et al. A high-performance, portable implementation of the MPI message passing interface standard. Parallel Computing,1996,22(6):789-828.
    [84]Freund RW, Golub GH, Nachtigal NM. Iterative solution of linear systems. Acta numerica,2008, (1):57-100.
    [85]Golub GH, O'Leary DP. Some history of the conjugate gradient and Lanczos methods. SIAM Review,1989,31(1):50-102.
    [86]Benzi M, Tuma M. A comparative study of sparse approximate inverse preconditioners. Applied Numerical Mathematics,1999,30(2):305-340.
    [87]Bank RE, Smith RK. An algebraic multilevel multigraph algorithm. SIAM Journal on Scientific Computing,2002,23(5):1572-1592.
    [88]Bank RE, Wagner C. Multilevel ILU decomposition. Numerische Mathematik,1999, 82(4):543-576.
    [89]Zhang J. Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices. Applied Numerical Mathematics,2000,35(1): 67.
    [90]Broker O, Grote MJ. Sparse approximate inverse smoothers for geometric and algebraic multigrid. Applied Numerical Mathematics,2002,41(1):61-80.
    [91]Xiao H, Chen Z. Numerical experiments of preconditioned Krylov subspace methods solving the dense non-symmetric systems arising from BEM. Engineering Analysis with Boundary Elements,2007,31(12):1013-1023.
    [92]Chen Z, Xiao H. Preconditioned Krylov Subspace Methods Solving Dense Nonsymmetric Linear Systems Arising from BEM. Lecture Notes in Computer Science,2007,4489:113.
    [93]Valente FP, Pina HL. Conjugate gradient methods for three-dimensional BEM systems of equations. Engineering Analysis with Boundary Elements,2006,30(6): 441-449.
    [94]Araujo FC, Silva KI, Telles JCF. Generic domain decomposition and iterative solvers for 3D BEM problems. Int J Numer Methods Eng,2006,68:448-472.
    [95]Yang YJ, Tang HK. A Parallelization Technique for Preconditioned Boundary-Element-Method Solvers. Journal of Electromagnetic Waves and Applications,2005,19(6):811-826.
    [96]Fischer M, Perfahl H, Gaul L. Approximate inverse preconditioning for the fast multipole BEM in acoustics. Computing and Visualization in Science,2005,8(3): 169-177.
    [97]Bebendorf M. Hierarchical LU decomposition-based preconditioners for BEM. Computing,2005,74(3):225-247.
    [98]Saitoh A, Kamitani A. GMRES with new preconditioning for solving BEM-type linear system. IEEE Transactions on Magnetics,2004,40(2 Part 2):1084-1087.
    [99]Buchau A, Rucker WM. Preconditioned fast adaptive multipole boundary-element method. IEEE Transactions on Magnetics,2002,38(2 Part 1):461-464.
    [100]Benzi M. Preconditioning techniques for large linear systems:a survey. Journal of Computational Physics,2002,182(2):418-477.
    [101]Valente FP, Pina HL. Iterative techniques for 3-D boundary element method systems of equations. Engineering Analysis with Boundary Elements,2001,25(6):423-429.
    [102]Benzi M, Cullum JK, Tuma M. Robust approximate inverse preconditioning for the conjugate gradient method. SIAM Journal on Scientific Computing,2001,22(4): 1318-1332.
    [103]Chen K. On a class of preconditioning methods for dense linear systems from boundary elements. SIAM Journal on Scientific Computing,1999,20(2):684-698.
    [104]M. Merkela, Bulgakova V, Bialeckib R, et al. Iterative solution of large-scale 3D-BEM industrial problems. Engineering Analysis with Boundary Elements,1998, 22:183-197.
    [105]Saad Y, Schultz MH. GMRES:A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput,1986,7(3):855-869.
    [106]Lim KM, He X, Lim SP. Fast Fourier transform on multipoles (FFTM) algorithm for Laplace equation with direct and indirect boundary element method. Computational Mechanics,2008,41(2):313-323.
    [107]Greengard L, Rokhlin V. A new version of the fast multipole method for the Laplace equation in three dimensions. Acta numerica,2008,6:229-269.
    [108]Buchau A, Tsafak SM, Hafla W, et al. Parallelization of a Fast Multipole Boundary Element Method with Cluster OpenMP. IEEE Transactions on Magnetics,2008, 44(6):1338-1341.
    [109]Liu YJ, Nishimura N. The fast multipole boundary element method for potential problems:A tutorial. Engineering Analysis with Boundary Elements,2006,30(5): 371-381.
    [110]Gonzalez P, Cabaleiro JC, Pena TF. Parallel iterative solvers involving fast wavelet transforms for the solution of BEM systems. Advances in Engineering Software, 2002,33(7-10):417-426.
    [111]Cheng H, Greengard L, Rokhlin V. A fast adaptive multipole algorithm in three dimensions. Journal of Computational Physics,1999,155(2):468-498.
    [112]吴恩华.图形处理器用于通用计算的技术现状及其挑战.软件学报,2004,15(10):205-214.
    [113]黄芳,樊晓平.基于岛屿群体模型的并行粒子群优化算法.控制与决策,2006,21(2):175-180.
    [114]赵勇,岳继光,李炳宇,等.一种新的求解复杂函数优化问题的并行粒子群算法.计算机工程与应用,2005,41(16):58-64.
    [115]钟慧湘,王钲旋,庞云阶.图象重建中的有理逼近方法.中国图象图形学报,2000,5A(11):915-919.
    [116]荆人杰,叶秀清,许胜荣.计算机图象处理.杭州:浙江大学出版社,1990:447-518.
    [117]冯兰,蔡英文,何丹农,余震.金属板料成形数值模拟的研究现状.塑性工程学报.2004,11(06):1-6.
    [118]Turetta, A., Bruschi, S., Ghiotti, A. Investigation of 22MnB5 formability in hot stamping operations. Journal of Materials Processing Technology.2006,177(1-3): 395-400.
    [119]Mori, K., Maki, S., Tanaka, Y. Warm and hot stamping of ultra high tensile strength steel sheets using resistance heating. CIRP Annals-Manufacturing Technology. 2005,54(1):209-212.
    [120]Gauchia, A., Alvarez-Caldas, C., Quesada, A., San Roman, J. L. Material parameters in a simulation of metal sheet stamping. Proceedings of the Institution of Mechanical Engineers, Part D:Journal of Automobile Engineering.2009,223(6):783-791.
    [121]Hare wood, F. J., McHugh, P. E. Comparison of the implicit and explicit finite element methods using crystal plasticity. Computational Materials Science.2007, 39(2):481-494.
    [122]Rama Mohan Rao, A. A parallel mixed time integration algorithm for nonlinear dynamic analysis. Advances in Engineering Software.2002,33(5):261-271.
    [123]Sun, J. S., Lee, K. H., Lee, H. P. Comparison of implicit and explicit finite element methods for dynamic problems. Journal of Materials Processing Technology.2000, 105(1-2):110-118.
    [124]Leblond, J. B., Mottet, G, Devaux, J. C. A theoretical and numerical approach to the plastic behaviour of steels during phase transformations--I. Derivation of general relations. Journal of the Mechanics and Physics of Solids.1986,34(4):395-409.
    [125]Wei, etc., Micromagnetics of ferromagnetic nano-devices using the fast fourier transform method Materials integrity in microsystems:A framework for a petascale predictive-science-based multiscale modeling and simulation system,2009: 3035-3045.
    [126]Wang, H., etc. The least square support vector regression coupled with parallel sampling scheme metamodeling technique and application in sheet forming optimization. Materials & Design.2009,30(5):1468-1479.
    [127]Tiesel, J.-P. A. S. Using parallel GPU architecture for simulation of planar I/F networks,.2009:Atlanta, GA, United states:3118-3123.
    [128]Sul, I. H., Ha, L. etc. Parallel garment drape simulation of triangular mesh using GPU programming Fast four-way parallel radix sorting on GPUs,2009:228-245.
    [129]Shen, W.etc. GPU-based parallelization for computer simulation of electrocardiogram,2009:280-284.
    [130]Sul, I. H., Parallel garment drape simulation of triangular mesh using GPU programming.2009:228-245.
    [131]Negrut. etc. Large-scale parallel multibody dynamics with frictional contact on the GPU.2009:Ann Arbor, MI, United states:347-354.
    [132]Li H. etc. Parallel simulation for a fish schooling model on a general-purpose graphics processing unit.2009:725-737.
    [133]宋久鹏,柳葆生.金属注射成形烧结工艺的试验与数值模拟.机械工程学报,2008,(08):157-163.
    [134]林建平,王立影,田浩彬,孙国华,王芝斌.超高强度钢板热冲压成形研究与进展.金属铸锻焊技术,2008,37(27):5.
    [135]Stantchev, etc. Fast parallel Particle-To-Grid interpolation for plasma PIC simulations on the GPU.2008:1339-1349.
    [136]Phillips, etc. Adapting a message-driven parallel application to GPU-accelerated clusters.2008:Austin, TX, United states:108-113
    [137]Perumalla, K. S. A. B. G, Data parallel execution challenges and runtime performance of agent simulations on GPUs.2008:Ottawa, ON, Canada:115-123.
    [138]Naderi, M., Uthaisangsuk, V., Prahl, U., Bleck, W. A numerical and experimental investigation into hot stamping of boron alloyed heat treated steels. Steel Research International.2008,79(2):77-84.
    [139]Ibrahim, K. Z. etc. Fine-grained parallelization of lattice QCD kernel routine on GPUs.2008:1350-1359.
    [140]Ho, T.etc. Parallelization of cellular neural networks on GPU.2008:2684-2692.
    [141]Groche, P., Kloepsch, C. Sheet metal forming processes at elevated temperatures. Journal of Advanced Manufacturing Systems.2008,7(2):307-311.
    [142]Gao, J. E. J., Parallel integration of planetary systems on GPUs.2008:Auburn, AL, United states:7-12.
    [143]吴欣,赵国群,管延锦,路平.反向挤压过程无网格伽辽金热力耦合分析.工程力学.2007,24(06):180-184.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700