机群环境下的并行边界元法研究及其在水工结构分析中的应用
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摘要
将并行计算技术引入结构的边界元分析，可以从很大程度上增大结构分析的规模，提高分析的速度，从而促进边界元法的大型工程应用和现场实时应用。本文主要在网络微机机群并行计算环境下，对弹性静力、弹性动力和弹塑性结构的并行边界元分析方法进行了研究，并在水工结构分析中进行了实际应用。全文主要内容如下：
(1)建立了一个简单易用的局域网微机机群并行计算环境，并给出了详细的计算环境配置和使用方法。
(2)提出了边界元系统方程组结点超行的概念，采用结点超行卷帘分布存储方案实现单域边界元系统方程组的并行形成和负载平衡，并在此分布存储方案的基础上改进了单域边界元系统方程组的内存并行高斯-若当消去法；引入内外存交互技术，发展了单域边界元外存并行分析算法，算法根据内存容量和工作区数，对数据进行分块，块内消元采用并行高斯-若当消去，块间采用环状循环修正消元；算法采用本地块内选主元技术平衡外存访问、通信和数值精度和稳定性之间的矛盾；程序设计阶段实现了内存和外存算法的统一和自动识别选用功能。
(3)采用重正交技术解决了经典GMRES方法在求解大型三维弹性静力边界元问题过程中出现的基向量正交性丧失的问题；结合边界元基本解和系数矩阵的特点以及并行化的要求，研究了几种预条件技术；并以重正交技术和预条件技术实现了经典GMRES的实用化。分析了经典GMRES算法的复杂度和并行性，提出了实用化技术和并行化技术结合使用的思想，通过对矩阵向量运算的分布并行处理实现了实用化GMRES算法的并行计算；编制了相应的串并行程序，进行了数值试验验证。
(4)给出了一种可以在计算的每一个阶段根据不同的计算规模和机群规模，自动识别选用内存或外存算法的边界元子域并行算法；实现了各主要计算步骤的并行化；对于剩余方程组的并行求解，算法可以在不改变当前数据分布状态下，实行并行求解。
(5)针对不同子域划分情况和机群配置情况，提出了两种不同并行粒度的负载平衡的子域并行算法：多域一机算法和多机一域算法；算法都是在对计算量和通信量进行评估和获取了机群性能后，将负载均衡分配，不同的只是负载的基本粒度不同，多域一机算法是以子域为基本分配单位，而多机一域算法则是以结点超行为基本单位。
(6)通过拉氏积分变换法将弹性动力问题转换至变换域，通过变换域上边界元的分布并行处理实现了弹性动力边界元分析的并行化；引入与时间有关的基本解，解除了时域边界元系统方程组形成阶段的时间顺序依赖性，通过矩阵向量运算的分布并行处理实现方程组时间步进求解方法的并行化，这种方法是一种部分时间并行算法。
(7)分析了弹塑性边界元计算各主要过程的计算复杂度和并行性；采用结点超行连续分布存储方案实现了方程系数矩阵的并行形成；通过对矩阵向量运算的并行化处理，研究并发展出了并行增量初应力迭代算法，实现了应力迭代方程的并行求解。
(8)将并行弹性静力边界元法应用于水工地下洞室的计算分析之中，进一步验正了算法的高效性和可靠性，显示了算法的应用价值。
The technology of parallel computation is introduced into the structure Boundary Element(BE) analysis to multiply the size of problem to solve, accelerate the analysis and facilitate the large-scale application and real-time application in the locale. Under the networked PC cluster parallel computing environment, the parallel Boundary Element Method(BEM) used to analyze elasto-static, elasto-dynamic and elasto-plastic structure is studied in this dissertation and applied to analysis of hydraulic structure. The main contents of this dissertation are as follows:
(1) A new networked PC cluster parallel computing environment is set up,which is simple and easy to use. The detailed method of configuration and use is presented.
(2) The concept of BEM equations node-super-row is presented. The node-super-row wrap distributed storage scheme is used to implement the BEM equations parallel formation and load balance. Based on this distributed storage, the in-core parallel Gauss-Jordan eliminating method of single domain BE equations is improved. An out-of-core algorithm to solve single domain BE equations is developed by interacting between in- and out-of-core. Based on the size of core and number of working space, the data is blocked. The parallel Gauss-Jordan eliminating method is used in the same block and the wrap cyclic modification method is presented for elimination between the different blocks. A local in-block pivoting technique is used in out-of-core algorithm to balance external memory access, communication, numerical stability and numerical accuracy. In the parallel program, the in-core and out-of-core algorithms can be identified and chosen to use automatically. So the algorithms are united.
(3) The re-orthonormalization technique is used to solve the loss of orthonormality of basis vector during the classical GMRES method solving large-scale three dimensional elasto-static BE problems. Based on the characteristic of fundamental solution and the coefficient matrix, several precondition methods are studied. By using the technique of re-orthonoramalization and precondition, the practical GMRES method is developed based on the classical one. The complexity and parallelism of the classical GMRES are analyzed. The idea of combining the practical technique with parallel technique is presented and the parallelization of practical GMRES is implemented. The corresponding serial and parallel programs are developed and different numerical tests are carried out.
(4) A BE sub-region parallel algorithm is presented. This algorithm can identify and choose in-core or out-of core algorithm based on different scale of computation and cluster during each computing phase. And parallelization during each phase is implemented. This algorithm can solve the residual equations parallelly and the current data distribution of residual equations does not change.
(5) Two load-balance sub-region parallel algorithms with different parallel granularity are presented to solve different combination of sub-region partition and cluster configuration. They are multi-domain-one-processor algorithm and multi-processor-one-sub-region algorithm. These algorithms all allocate tasks uniformly based on the evaluation of computational load and the parameters of cluster. The difference between these two algorithms is that the former uses sub-domain
as the basic unit of task to be allocated and the latter uses the node-super-row as the basic unit of task.
(6) The original problem is transformed into transformed domain by using Laplace transform method. By the parallelization of the BEM in the transformed domain, the parallelization of the elasto-dynamic BE analysis is implemented By introducing the time related fimdamental solution, the time dependency is released from the formation of time-domain BE equations. The time stepping method is parallelized by distributed parallelization of the matrical computing. The parallel time-domain BEM is a partial time-parallel algorithm.
(7) The computational complexity and parallelism of t
(1)建立了一个简单易用的局域网微机机群并行计算环境，并给出了详细的计算环境配置和使用方法。
(2)提出了边界元系统方程组结点超行的概念，采用结点超行卷帘分布存储方案实现单域边界元系统方程组的并行形成和负载平衡，并在此分布存储方案的基础上改进了单域边界元系统方程组的内存并行高斯-若当消去法；引入内外存交互技术，发展了单域边界元外存并行分析算法，算法根据内存容量和工作区数，对数据进行分块，块内消元采用并行高斯-若当消去，块间采用环状循环修正消元；算法采用本地块内选主元技术平衡外存访问、通信和数值精度和稳定性之间的矛盾；程序设计阶段实现了内存和外存算法的统一和自动识别选用功能。
(3)采用重正交技术解决了经典GMRES方法在求解大型三维弹性静力边界元问题过程中出现的基向量正交性丧失的问题；结合边界元基本解和系数矩阵的特点以及并行化的要求，研究了几种预条件技术；并以重正交技术和预条件技术实现了经典GMRES的实用化。分析了经典GMRES算法的复杂度和并行性，提出了实用化技术和并行化技术结合使用的思想，通过对矩阵向量运算的分布并行处理实现了实用化GMRES算法的并行计算；编制了相应的串并行程序，进行了数值试验验证。
(4)给出了一种可以在计算的每一个阶段根据不同的计算规模和机群规模，自动识别选用内存或外存算法的边界元子域并行算法；实现了各主要计算步骤的并行化；对于剩余方程组的并行求解，算法可以在不改变当前数据分布状态下，实行并行求解。
(5)针对不同子域划分情况和机群配置情况，提出了两种不同并行粒度的负载平衡的子域并行算法：多域一机算法和多机一域算法；算法都是在对计算量和通信量进行评估和获取了机群性能后，将负载均衡分配，不同的只是负载的基本粒度不同，多域一机算法是以子域为基本分配单位，而多机一域算法则是以结点超行为基本单位。
(6)通过拉氏积分变换法将弹性动力问题转换至变换域，通过变换域上边界元的分布并行处理实现了弹性动力边界元分析的并行化；引入与时间有关的基本解，解除了时域边界元系统方程组形成阶段的时间顺序依赖性，通过矩阵向量运算的分布并行处理实现方程组时间步进求解方法的并行化，这种方法是一种部分时间并行算法。
(7)分析了弹塑性边界元计算各主要过程的计算复杂度和并行性；采用结点超行连续分布存储方案实现了方程系数矩阵的并行形成；通过对矩阵向量运算的并行化处理，研究并发展出了并行增量初应力迭代算法，实现了应力迭代方程的并行求解。
(8)将并行弹性静力边界元法应用于水工地下洞室的计算分析之中，进一步验正了算法的高效性和可靠性，显示了算法的应用价值。
The technology of parallel computation is introduced into the structure Boundary Element(BE) analysis to multiply the size of problem to solve, accelerate the analysis and facilitate the large-scale application and real-time application in the locale. Under the networked PC cluster parallel computing environment, the parallel Boundary Element Method(BEM) used to analyze elasto-static, elasto-dynamic and elasto-plastic structure is studied in this dissertation and applied to analysis of hydraulic structure. The main contents of this dissertation are as follows:
(1) A new networked PC cluster parallel computing environment is set up,which is simple and easy to use. The detailed method of configuration and use is presented.
(2) The concept of BEM equations node-super-row is presented. The node-super-row wrap distributed storage scheme is used to implement the BEM equations parallel formation and load balance. Based on this distributed storage, the in-core parallel Gauss-Jordan eliminating method of single domain BE equations is improved. An out-of-core algorithm to solve single domain BE equations is developed by interacting between in- and out-of-core. Based on the size of core and number of working space, the data is blocked. The parallel Gauss-Jordan eliminating method is used in the same block and the wrap cyclic modification method is presented for elimination between the different blocks. A local in-block pivoting technique is used in out-of-core algorithm to balance external memory access, communication, numerical stability and numerical accuracy. In the parallel program, the in-core and out-of-core algorithms can be identified and chosen to use automatically. So the algorithms are united.
(3) The re-orthonormalization technique is used to solve the loss of orthonormality of basis vector during the classical GMRES method solving large-scale three dimensional elasto-static BE problems. Based on the characteristic of fundamental solution and the coefficient matrix, several precondition methods are studied. By using the technique of re-orthonoramalization and precondition, the practical GMRES method is developed based on the classical one. The complexity and parallelism of the classical GMRES are analyzed. The idea of combining the practical technique with parallel technique is presented and the parallelization of practical GMRES is implemented. The corresponding serial and parallel programs are developed and different numerical tests are carried out.
(4) A BE sub-region parallel algorithm is presented. This algorithm can identify and choose in-core or out-of core algorithm based on different scale of computation and cluster during each computing phase. And parallelization during each phase is implemented. This algorithm can solve the residual equations parallelly and the current data distribution of residual equations does not change.
(5) Two load-balance sub-region parallel algorithms with different parallel granularity are presented to solve different combination of sub-region partition and cluster configuration. They are multi-domain-one-processor algorithm and multi-processor-one-sub-region algorithm. These algorithms all allocate tasks uniformly based on the evaluation of computational load and the parameters of cluster. The difference between these two algorithms is that the former uses sub-domain
as the basic unit of task to be allocated and the latter uses the node-super-row as the basic unit of task.
(6) The original problem is transformed into transformed domain by using Laplace transform method. By the parallelization of the BEM in the transformed domain, the parallelization of the elasto-dynamic BE analysis is implemented By introducing the time related fimdamental solution, the time dependency is released from the formation of time-domain BE equations. The time stepping method is parallelized by distributed parallelization of the matrical computing. The parallel time-domain BEM is a partial time-parallel algorithm.
(7) The computational complexity and parallelism of t
引文
1．刘金水，并行处理机技术及其挑战，中国计算机用户，1991(10)：2-5
2．周毓麟，沈隆钧，高性能计算的应用及战略地位，中国科学院院刊，1999(3)：184～187
3. Dimitris Zois, Parallel processing techniques for FE analysis: stiffness, loads and stress evaluation, Computers & Structures, 1988,28(2): 247～260
4. E Barragy, Graham F Carey, A parallel element-by-element solution scheme, Int. J. Numer. Methods Eng., 1988,26:2367～2381
5. M Lesoinne, C Farhat, M Geradin, Parallel/vector improvements of the frontal method, Int. J. Numer. Methods Eng., 1991,32:1267～1281
6. S Bitzarakis, M Papadrakakis, A Kotsopulos, Parallel solution techniques in computational structural mechanics, Comput. Methods Appl. Mech. Engrg., 1997,148:75～104
7. P Geng, J T Oden, R A van de Geijin, A parallel multifrontal algorithm and its implementation, Comput. Methods Appl. Mech. Engrg., 1997,149:289～301
8. Jennifer A Scott, A parallel frontal solver for finite element applications, Int. J. Numer. Methods Eng., 2001,50:1131～1144
9. L S Chien, C T Sun, Parallel processing techniques for finite element analysis of nonliear large truss structures, Computers & Structures, 1989,31(6): 1023～1029
10. N J Sorensen, B S Andersen, A parallel finite element method for the analysis of crystalline solids, Comput. Methods Appl. Mech. Engrg,, 1996,132:345～357
11. Olaf Storaasli, Jonathan Ransom, Robert Fulton, Structural dynamic analysis on a parallel computer: the finite element machine, Computers & Structures, 1987,26(4): 551～559
12. Ronfu Ou, Robert E Fulton, An investigation of parallel numerical integration methods for nonlinear dynamics, Computers & Structures, 1988,30(1/2): 403～449
13. Jerrome F Hajjar, John F Abel, Parallel processing for transient nonlinear structural dynamics of three-dimensional flamed stuetures using domain decomposition, Computers & Structures, 1988,30(6): 1237～1254
14. Ali Namazifard, I D Parsons, An MPI parallel implementation of Newmak's method, Computer-Aided Civil and Infrastructure Engineering, 2000,15:189～195
15. Petr Krysl, Zdenek Bittnar, Parallel explicit finite element solid dynamics with domain decomposition and message passing: dual partioning scalability, Computers and Structures, 2001,79:345～360
16. Ame S Gullerud, Robert H Dodds Jr, MPI-based implementation of a PCG solver using an EBE architecture and preconditioner for implicit, 3-D finite element analysis, Computers and Structures, 2001,79:553～575
17. B A Schrefler, R Matteazzi, D Gawin, X Wang, Two parallel computing methods for coupled thermohydromechanical problems, Computer-Aided Civil and Infrastructure Engineering,
2000,15:176～188
18. C T Sun, K M Mao, Elastic-plastic crack analysis using a global-local apppmach on parallel computer, Computers & Structures, 1988,30(1/2): 395～401
19. C Ozturan, H L deCougny, M S Shephard, J E Flaherty, Parallel adaptive mesh refinement and redistribution on distributed memory computers, Comput. Methods Appl. Mech. Engrg., 1994,119: 123～137
20. J T Oden, Abani Patra, A parallel adaptive strategy for hp finite element computations, Comput. Methods Appl. Mech. Engrg., 1995,121: 449～470
21. Xian Z Guo, Kent W Myers, A parallel solver for the hp-version of finite element methods, Comput. Methods Appl. Mech. Engrg., 1996,133:229～246
22. M Papadmkakis, A Kotsopulos, Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation, Comput. Methods Appl. Mech. Engrg., 1999,168:305～320
23. Raninald Lohner, Jose Camberos, Marshal Merriam, Parallel unstructured grid generation, Computer Methods in Applied Mechanics and Engineering, 1992,95:343～357
24. R Said, N P Weatherill, K Morgan, N A Verhoeven, Distributed parallel delaunay mesh generation, Comput. Methods Appl. Mech. Engrg., 1999,177:109～125
25. K Morgan, P J Brookes, O Hassan, N P Weatherill, Parallel processing for the simulation of problems involving scattering of electmmagetic waves, Comput. Methods Appl. Mech. Engrg., 1998,152:157～174
26．李晓梅等编著，面向结构的并行算法—设计与分析，长沙：国防科技大学出版社，1996
27．陈国良编著，并行计算—结构．算法．编程，北京：高等教育出版社，1999
28. Li G, Colemen T, A parallel triangular solver for a distributed-memory multiprocessor, SIAM J. Sci. Statists. Comput., 1988,9(3): 558～588.
29. Fiebach P, Cyclic block-algorithms for solving triangular system on distributed-memory message-passing multiprocessors, Parallel Comput., 1996,22(3): 383～393.
30．骆志刚，李晓梅，胡庆丰，三角形方程组的一种分布式并行算法，计算机工程与设计，2000，21(6)：54～59
31．武支耀，徐甲同，局部列主元消去算法的设计与实现—基于PVM的稠密线性方程组求解的并行算法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，204～210
32．迟学斌，Transputer上线性系统的并行求解，中国计算机用户，1991(10)：17～20
33．迟学斌，LU分解的高效实现方法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，137～142
34．裴伟东，求解稠密线性方程组的并行算法研究，天津师大学报(自然科学版)，1998，18(3)：20～25
35. T J Urekew, J J Rencis, A hybrid equation solver for BEM, In: C. A. Brebbia, J. J. Rencis ed. Boundary Element XV, Southampton: Computational Mechanics Publications, 1993:529～549
36. Szyld D B, Jones M T, Two-stage and multisplitting methods for the parallel solution of linear system, SIAM J. Matrix Anal. Appl., 1992,13:671～679
37．谷同祥，王能超，并行求解线性方程组的非定常二级多分裂迭代方法，工程数学学报，1997，14(4)：25～32
38. Wang H H, A parallel method for triagonal equations, ACM Trans on Mathematical Software, 1981,7(2): 170～183
39. Ho C, Johnson S, Optimizing triagonal solver alternating direction methods on Boolean cube multiprocessors, SIAM Journal on Scientific and Statistical Computing, 1990,11(3): 563～592
40. Michielse P H, Vander Vorst H A, Data transport on Wang's partition method, Parallel Computing, 1988,7(1): 87～95
41．侯英，李晓梅，三对角方程组并行求解策略，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，181～186
42．侯英，李晓梅，马欣明，工作站网络下三对角方程组并行求解，计算机工程与设计，1998，19(1)：52-58
43．迟利华，李晓梅，三对角线性方程组的分布式并行算法，计算机研究与发展，1998，35(11)：1004～1007
44．骆志刚，李晓梅，王正华，三对角线性方程组的一种有效分布式并行算法，计算机研究与发展，2000，37(7)：802～806
45．骆志刚，李晓梅，块三对角线性方程组的一种分布式并行算法，计算机学报，2000，23(10)：1028～1034
46．吕全义，叶天麒，系数矩阵为块三对角的线性方程组地并行算法，西北工业大学学报，1996，14(2)：315～318
47．李长虹，徐甲同，多处理机中三对角方程组的分块迭代并行算法，西安电子科技大学学报，1995，22(1)：21～26
48. Yanis S. Roditis and Panos D. Kiousis, Parallel multisplitting block Jacobi type solutions of linear systems of equations, Inter. Jour. For Numer. Meth. In Engin., 1990,29:619～632
49．吴建平，李晓梅，带状线性方程组地并行分裂算法，指挥技术学院学报，2000，12(5)：88～92
50．宋晓秋，求解一般带状线性方程组的解耦分解并行算法，计算机工程与设计，1995，16(5)：51～56
51．李晓梅，迟利华，并行求解大型稀疏线性方程组的研究概况，指挥技术学院学报，1999，10(3)：1～8
52．熊新平，并行预条件GMRES方法，计算机工程与设计，1994，(4)：25～32
53．刘兴平，非对称线性代数方程组的并行算法，计算物理，1994，11(3)：353～361
54．刘兴平，非对称线性代数方程组的块向量算法，应用数学与计算数学学报，1995，9(2)：60～67
55．刘兴平，胡家赣，块多分裂方法与预条件子空间迭代方法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，125～131
56．刘青昆，舒继武，张德富，Krylov子空间方法解线性方程组的并行性能分析及应用，计算
机工程与应用，1999(6)：33～36
57．陈景良，顾圣，大型对称稀疏线性方程组的Lanczos型算法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，132～136
58．刘兴平，胡家赣，块多分裂方法与预条件子空间迭代方法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，125～131
59．迟学斌，Transputer上Cholesky分解的并行实现，计算数学，1993(3)：289～294
60．王顺绪，周树荃，卷帘行存储下的一种并行Cholesky分解及其在PAR95上的实现，南京航空航天大学学报，1999，31(4)：428～433
61．梁维泰，周树荃，对称带状矩阵的并行Cholesky分解及相应线性方程组的并行计算，南京航空航天大学学报，1991，23(2)：133～138
62．张健飞，姜弘道，带状对称正定矩阵的并行Cholesky分解及其实现，第七届全国并行计算学术交流会，成都，2002，7
63．王荩贤，有限元结构分析在MIMD计算机上的并行直接解法，计算数学，1991(4)：433～438
64. Kincho H Law and David R Mackay, Parallel row-oriented sparse solution method for finite element structural analysis, Inter. Jour. For Numer. Meth. In Engin., 1993,36:2895～2919
65．王思群，魏紫銮，Cholesky分解求解大型稀疏线性方程组的并行算法，数值计算与计算机应用，1996(2)：104～111
66．杜庆华等著，边界积分方程方法—边界元法．北京：高等教育出版社，1989
67. Das P C A, Disk-based block elimination technique used for the solution of nonsymmetrical fully populated matrix systems encountered in the boundary element method, In: C. A. Brebbia ed, Recent Advances in Boundary Element Methods, London: Pentech Press, 1978:391～404
68. M M Stabrowski, A block equation solver for large unsymmetric linear equation systems with dense coefficient matrices, Int. J. Numer. Methods Eng., 1987,24:289～300
69. M Rezayat, Fast decomposition of matrices generated by boundary element method, Int. J. Numer. Methods Eng., 1992,33:1109～1118
70．袁驷，边界元法中非对称满系数矩阵方程组的拟波阵解法及程序，计算结构力学及其应用，1986，3(1)：105～108
71．曹平，陈爱华，边界元法中线性方程组的拟波阵分块求解，计算力学学报，1999，16(1)：41～46
72. Lachat J C, Watson J O, Progress in the use of boundary integral equation illustrated by examples, Computer Methods in Applied Mechanics and Engineering, 1977,10:273～389
73. J M Cmtty, A block equation solver for large unsyrnmetric matrices arising in the boundary integral equation method, Int. J. Numer. Methods Eng., 1982,18:997-1017
74. R Bialecki, Linear equation solver for large block matrices arising in BEM, In: C A Brebbia, W L Wendland, G Kuhn ed, Boundary Element Ⅸ: Mathematical and Computational Aspects, Southampton: Computational Mechanics Publications, 1987:493～504
75. R H Rigby, M H Aliabadi, Out-of-core solver for large, multi-zone boundary element matrices, Int. J. Numer. Methods Eng., 1995,38:1507～1533
76. J H Kane, B L Kashava Kumar, Sunil Saigal, An arbitrary condensing, noncondensing solution strategy for large scale, multi-zone boundary element analysis, Computer Methods in Apllied Mechanics and Engineering, 1990,79:219～244
77. Ryszard A Bialecki, Markus Merkel, Horst Mews, Guther Kuhn, In- and out-of-core BEM equation solver with parallel and non-linear options, Int. J. Numer. Methods Eng., 1996,39: 4215～4242
78．吴旭光，徐汉忠，非均质问题的边界元不求逆的凝聚解法，河海大学学报，1994，22(2)：93～96
79．张效松，叶天麒，二维边界元奇异积分和多域缩聚法分析，计算力学学报，1997，14(2)：196～203
80．张效松，叶天麒，三维弹性力学边界元多域缩聚法分析，应用力学学报，1998，15(1)：16～22
81. F C Araujo, W J Mansur, Iterative solver for BEM systems of equations, In: C A Brebbia, J J Connor ed, Advances in Boundary Element: Computations and Fundamentals, Southampton: Computational Mechanics Publications, 1989, 263～274
82. F C Araujo, W J Mansur, J E B Malaghini, Biconjugate gradient acceleration for large BEM systems of equations, M Tanaka, C A Brebbia, T Honma ed, Boundary Element Ⅻ: Stress Analysis, Potential and Diffusion, Southampton: Computational Mechanics Publications, 1990: 99～110
83. F P Valente, H L G Pina, Iterative solvers for tridimensional BEM algebraic systems of equations, In: C A Brebbia, J B Martins, M H Aliabadi, N Haie ed, Boundary Element ⅩⅧ, Southampton: Computational Mechanics Publications, 1996:269～278
84. L P S Barra, W J Mansur, A L G A Coutinho, J C F Telles, Preconditioning techniques for iterative solutions of BEM systems of equations, In: C A Brebbia, J Dominguez, F Paris ed, Boundary Element ⅩⅣ Vol. 2: Stress Analysis and Computational Aspects, Southampton: Computational Mechanics Publications, 1992:643～650
85. C Y Leung, S P Walker, Iterative solution of large three-dimensional BEM elastostatic analyses using the GMRES technique, Int. J. Numer. Methods Eng., 1997,40:2227～2236
86. S Amini, N D Maines, Preconditioned krylov subspace methods for boundary element solution of the Helmholtz equation, Int. J. Numer. Methods Eng., 1996,41:875～898
87. N S Jovanovic, D E Keyes, K Guru Prasad, J H Kane, Drop tolerance ILU preconditioners for iterative solution techniques in boundary element analysis, In: C A Brebbia, J J Rencis ed, Boundary Element ⅩⅤ: Fluid Flow and Computational Aspects, Southampton: Computational Mechanics Publications, 1993:501～516
88．王人鹏，沈祖炎，钱若军，应用Krylov子空间方法求解边界元方程组，同济大学学报，1997，25(2)：212～217
89. J H Kane, D E Keyes, K Guru Prasad, Iterative solution techniques in boundary element analysis, Int. J. Numer. Methods Eng., 1991,31:1511～1536
90. K Guru Prasad, J H Kane, D E Keyes, C Balakrishna, Preconditioned krylov solvers for BEA, Int.
J. Numer. Methods Eng., 1994,37:1651～1672
91. F C de Araujo, G J Belmonte, M S R Freitas, On the use of iterative solvers for generating efficient 3D multidomain boundary element algorithms, In: C A Brebbia, H Power ed. Boundary Element ⅩⅪ, Southampton: WIT Press, 1999:219～228
92. N S Jovanovic, D E Keyes, K Guru Prasad, J H Kane, Drop tolerance ILU preconditioners for iterative solution techniques in boundary element analysis, In: C A Brebbia, J J Rencis ed, Boundary Element ⅩⅤ: Fluid Flow and Computational Aspects, Southampton: Computational Mechanics Publications, 1993:501～516
93. T J Urekew, J J Rencis, A hybrid equation solver for BEM, In: C A Brebbia, J J Rencis ed, Boundary Element ⅩⅤ: Fluid Flow and Computational Aspects, Southampton: Computational Mechanics Publications, 1993:529～549
94. Symm G T, Boundary elements on a distributed army processor, Engineering Analysis, 1984,1: 162～165
95. Davies A J, The boundary element method on the ICL DAP, Parallel Computing, 1988,8: 348～353
96. A J Davies, The boundary element method on a transputer network, In: C A Brebbia, G S Gipson ed, Boundary Element ⅩⅢ, Southampton: Computational Mechanics Publications, 1991: 985～994
97. Alberto Zucchini, Subrata Mukherjee, Vectorial and parallel processing in stress analysis with the boundary element method, Int. J. Numer. Methods Eng., 1991,31: 307～317
98. J M Cela, A Julia, High performance computing on boundary element simulations, In: C A Brebbia, H Power ed, Boundary Element ⅩⅫ, Southampton: WIT Press, 2000:175～179
99. A J Davies, A parallel implementation of the dual reciprocity boundary element method, In: C A Brebbia, J Dominguez, F Paris ed, Boundary Element ⅩⅧ Vol. 2: Stress Analysis and Computational Aspects, Southampton: Computational Mechanics Publications, 1992:613～626
100．尹欣，姚振汉，程建钢，基于微机机群网络的边界元并行计算，重庆建筑大学学报，2000，22(6)：92～95
101．姚振汉，蒲军平，尹欣，段小华，边界元法应用的若干近期研究，力学季刊，2001，22(1)：10～17
102. M S Ingber, D E Womble, A parallel iterative equation solver for the analysis of suspension flows using the boundary element method, In: M Marchetti, C A Brebbia, M H Aliabadi ed, Boundary Element ⅩⅠⅩ, Southampton: Computational Mechanics Publications, 1997:583～592
103. K A Kline, N K Tsao, C B Friedlander, Parallel processing and the solution of boundary element equations, In: T A Cruse, A B Pifko, H Armen ed, Advanced Topic In Boundary Element Analysis, New York: The American Society of Mechanical Engineers, 1985:257～270
104. N Kamiya, H Iwase, E Kita, Parallel algorithm for BEM analysis, In: C A Brebbia, J B Martins, M H Aliabadi, N Haie ed, Boundary Element ⅩⅧ, Southampton: Computational Mechanics Publications, 1996:163～171
105. N Kamiya, H Iwase, Boundary element domain decomposition method and its parallelization for the problem exhibiting nonlinear boundary conditions, In: M. Marchetti, C A Brebbia, M H Aliabadi ed, Boundary Element ⅩⅠⅩ, Southampton: Computational Mechanics Publications, 1997:573～582
106. D Crann, A J Davies and J Mushtaq, Parallel Laplace transform boundary element methods for diffusion problem, In: A Kassab, C A Brebbia, M Chopin ed, Boundary Element ⅩⅩ, Southampton: Computational Mechanics Publications, 1998:259～268
107. A J Davies, D Crann, J Mushtaq, A parallel implementation of the Laplace transform BEM, In: C A Brebbia, J B Martins, M H Aliabadi, N Haie ed, Boundary Element ⅩⅧ, Southampton: Computational Mechanics Publications, 1996:163～171
108. C Catlett, L Smarr, Metacomputing, Comm. of ACM, 1992,35(6): 44～52
109. T E Anderson, D E Culler, D A Patterson et al, A case for NOW(Networks of Workstations), IEEE Micro, 1995,(4): 54～64
110. C Amza, A L Cox, S D Warkadas et al, TreadMarks: Shared memory computing on networks of workstations, IEEE Computer, 1996,29(2): 18～28
111．戴光明，戴晓明，基于PVM的微机网络并行计算及其应用，计算机工程与应用，2000，(9)：154～156
112．王莹，屈一新，PC集群的建立与MPI并行环境的实现及其应用，北京化工大学学报，2001，28(4)：4～6
113．黎康保，陶文正等，用PC机群组构并行超级计算机，计算机工程，2000，26(9)：1～3
114．岳光来，杨耀忠等，局域网分布式并行计算环境的建立与应用，计算机工程与应用，2002，(4)：136-138
115．张效松，叶天麒，葛守廉，边界积分方程—非连续边界元离散方法及其应用，计算力学学报，2001，18(3)：331～334
116．杜庆华等著，边界积分方程方法——边界元法，北京：高等教育出版社，1989
117．C．A．布瑞比亚等著，边界单元法的理论和工程应用，北京：国防工业出版社，1988
118．Cao Zhihao，Chen Guangxi，Hou Xiaodong,A convergent restarted GMRES algorithm，复旦大学学报(自然科学版)，1997，36(6)：645～651
119. L Wang, A. Semlyen, Applacation of sparse eigenvalue techniques to the small signal stability analysis of large power systems, IEEE Trans. Power Systems, 1990(5): 635～642
120. J W Daniel, W B Gragg, L Kattfinan, G W Stewart, Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factodzafion, Mathematics of Computation, 1976,30(136): 772～795
121．G．D马诺利斯，D E贝斯科思，弹性动力的边界元法，天津：天津科学技术出版社，1991
122. George D Manolis, A comparative study on three boundary element method approaches to problems in elastodynamies, Int. J. Numer. Methods Eng., 1983,19:73～91
123．王有成编，工程中的边界元方法，北京：中国水利水电出版社，1996
2．周毓麟，沈隆钧，高性能计算的应用及战略地位，中国科学院院刊，1999(3)：184～187
3. Dimitris Zois, Parallel processing techniques for FE analysis: stiffness, loads and stress evaluation, Computers & Structures, 1988,28(2): 247～260
4. E Barragy, Graham F Carey, A parallel element-by-element solution scheme, Int. J. Numer. Methods Eng., 1988,26:2367～2381
5. M Lesoinne, C Farhat, M Geradin, Parallel/vector improvements of the frontal method, Int. J. Numer. Methods Eng., 1991,32:1267～1281
6. S Bitzarakis, M Papadrakakis, A Kotsopulos, Parallel solution techniques in computational structural mechanics, Comput. Methods Appl. Mech. Engrg., 1997,148:75～104
7. P Geng, J T Oden, R A van de Geijin, A parallel multifrontal algorithm and its implementation, Comput. Methods Appl. Mech. Engrg., 1997,149:289～301
8. Jennifer A Scott, A parallel frontal solver for finite element applications, Int. J. Numer. Methods Eng., 2001,50:1131～1144
9. L S Chien, C T Sun, Parallel processing techniques for finite element analysis of nonliear large truss structures, Computers & Structures, 1989,31(6): 1023～1029
10. N J Sorensen, B S Andersen, A parallel finite element method for the analysis of crystalline solids, Comput. Methods Appl. Mech. Engrg,, 1996,132:345～357
11. Olaf Storaasli, Jonathan Ransom, Robert Fulton, Structural dynamic analysis on a parallel computer: the finite element machine, Computers & Structures, 1987,26(4): 551～559
12. Ronfu Ou, Robert E Fulton, An investigation of parallel numerical integration methods for nonlinear dynamics, Computers & Structures, 1988,30(1/2): 403～449
13. Jerrome F Hajjar, John F Abel, Parallel processing for transient nonlinear structural dynamics of three-dimensional flamed stuetures using domain decomposition, Computers & Structures, 1988,30(6): 1237～1254
14. Ali Namazifard, I D Parsons, An MPI parallel implementation of Newmak's method, Computer-Aided Civil and Infrastructure Engineering, 2000,15:189～195
15. Petr Krysl, Zdenek Bittnar, Parallel explicit finite element solid dynamics with domain decomposition and message passing: dual partioning scalability, Computers and Structures, 2001,79:345～360
16. Ame S Gullerud, Robert H Dodds Jr, MPI-based implementation of a PCG solver using an EBE architecture and preconditioner for implicit, 3-D finite element analysis, Computers and Structures, 2001,79:553～575
17. B A Schrefler, R Matteazzi, D Gawin, X Wang, Two parallel computing methods for coupled thermohydromechanical problems, Computer-Aided Civil and Infrastructure Engineering,
2000,15:176～188
18. C T Sun, K M Mao, Elastic-plastic crack analysis using a global-local apppmach on parallel computer, Computers & Structures, 1988,30(1/2): 395～401
19. C Ozturan, H L deCougny, M S Shephard, J E Flaherty, Parallel adaptive mesh refinement and redistribution on distributed memory computers, Comput. Methods Appl. Mech. Engrg., 1994,119: 123～137
20. J T Oden, Abani Patra, A parallel adaptive strategy for hp finite element computations, Comput. Methods Appl. Mech. Engrg., 1995,121: 449～470
21. Xian Z Guo, Kent W Myers, A parallel solver for the hp-version of finite element methods, Comput. Methods Appl. Mech. Engrg., 1996,133:229～246
22. M Papadmkakis, A Kotsopulos, Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation, Comput. Methods Appl. Mech. Engrg., 1999,168:305～320
23. Raninald Lohner, Jose Camberos, Marshal Merriam, Parallel unstructured grid generation, Computer Methods in Applied Mechanics and Engineering, 1992,95:343～357
24. R Said, N P Weatherill, K Morgan, N A Verhoeven, Distributed parallel delaunay mesh generation, Comput. Methods Appl. Mech. Engrg., 1999,177:109～125
25. K Morgan, P J Brookes, O Hassan, N P Weatherill, Parallel processing for the simulation of problems involving scattering of electmmagetic waves, Comput. Methods Appl. Mech. Engrg., 1998,152:157～174
26．李晓梅等编著，面向结构的并行算法—设计与分析，长沙：国防科技大学出版社，1996
27．陈国良编著，并行计算—结构．算法．编程，北京：高等教育出版社，1999
28. Li G, Colemen T, A parallel triangular solver for a distributed-memory multiprocessor, SIAM J. Sci. Statists. Comput., 1988,9(3): 558～588.
29. Fiebach P, Cyclic block-algorithms for solving triangular system on distributed-memory message-passing multiprocessors, Parallel Comput., 1996,22(3): 383～393.
30．骆志刚，李晓梅，胡庆丰，三角形方程组的一种分布式并行算法，计算机工程与设计，2000，21(6)：54～59
31．武支耀，徐甲同，局部列主元消去算法的设计与实现—基于PVM的稠密线性方程组求解的并行算法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，204～210
32．迟学斌，Transputer上线性系统的并行求解，中国计算机用户，1991(10)：17～20
33．迟学斌，LU分解的高效实现方法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，137～142
34．裴伟东，求解稠密线性方程组的并行算法研究，天津师大学报(自然科学版)，1998，18(3)：20～25
35. T J Urekew, J J Rencis, A hybrid equation solver for BEM, In: C. A. Brebbia, J. J. Rencis ed. Boundary Element XV, Southampton: Computational Mechanics Publications, 1993:529～549
36. Szyld D B, Jones M T, Two-stage and multisplitting methods for the parallel solution of linear system, SIAM J. Matrix Anal. Appl., 1992,13:671～679
37．谷同祥，王能超，并行求解线性方程组的非定常二级多分裂迭代方法，工程数学学报，1997，14(4)：25～32
38. Wang H H, A parallel method for triagonal equations, ACM Trans on Mathematical Software, 1981,7(2): 170～183
39. Ho C, Johnson S, Optimizing triagonal solver alternating direction methods on Boolean cube multiprocessors, SIAM Journal on Scientific and Statistical Computing, 1990,11(3): 563～592
40. Michielse P H, Vander Vorst H A, Data transport on Wang's partition method, Parallel Computing, 1988,7(1): 87～95
41．侯英，李晓梅，三对角方程组并行求解策略，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，181～186
42．侯英，李晓梅，马欣明，工作站网络下三对角方程组并行求解，计算机工程与设计，1998，19(1)：52-58
43．迟利华，李晓梅，三对角线性方程组的分布式并行算法，计算机研究与发展，1998，35(11)：1004～1007
44．骆志刚，李晓梅，王正华，三对角线性方程组的一种有效分布式并行算法，计算机研究与发展，2000，37(7)：802～806
45．骆志刚，李晓梅，块三对角线性方程组的一种分布式并行算法，计算机学报，2000，23(10)：1028～1034
46．吕全义，叶天麒，系数矩阵为块三对角的线性方程组地并行算法，西北工业大学学报，1996，14(2)：315～318
47．李长虹，徐甲同，多处理机中三对角方程组的分块迭代并行算法，西安电子科技大学学报，1995，22(1)：21～26
48. Yanis S. Roditis and Panos D. Kiousis, Parallel multisplitting block Jacobi type solutions of linear systems of equations, Inter. Jour. For Numer. Meth. In Engin., 1990,29:619～632
49．吴建平，李晓梅，带状线性方程组地并行分裂算法，指挥技术学院学报，2000，12(5)：88～92
50．宋晓秋，求解一般带状线性方程组的解耦分解并行算法，计算机工程与设计，1995，16(5)：51～56
51．李晓梅，迟利华，并行求解大型稀疏线性方程组的研究概况，指挥技术学院学报，1999，10(3)：1～8
52．熊新平，并行预条件GMRES方法，计算机工程与设计，1994，(4)：25～32
53．刘兴平，非对称线性代数方程组的并行算法，计算物理，1994，11(3)：353～361
54．刘兴平，非对称线性代数方程组的块向量算法，应用数学与计算数学学报，1995，9(2)：60～67
55．刘兴平，胡家赣，块多分裂方法与预条件子空间迭代方法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，125～131
56．刘青昆，舒继武，张德富，Krylov子空间方法解线性方程组的并行性能分析及应用，计算
机工程与应用，1999(6)：33～36
57．陈景良，顾圣，大型对称稀疏线性方程组的Lanczos型算法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，132～136
58．刘兴平，胡家赣，块多分裂方法与预条件子空间迭代方法，见：并行计算专业委员会编，第五届全国并行计算学术会议论文集，西安：陕西科学技术出版社，1997，125～131
59．迟学斌，Transputer上Cholesky分解的并行实现，计算数学，1993(3)：289～294
60．王顺绪，周树荃，卷帘行存储下的一种并行Cholesky分解及其在PAR95上的实现，南京航空航天大学学报，1999，31(4)：428～433
61．梁维泰，周树荃，对称带状矩阵的并行Cholesky分解及相应线性方程组的并行计算，南京航空航天大学学报，1991，23(2)：133～138
62．张健飞，姜弘道，带状对称正定矩阵的并行Cholesky分解及其实现，第七届全国并行计算学术交流会，成都，2002，7
63．王荩贤，有限元结构分析在MIMD计算机上的并行直接解法，计算数学，1991(4)：433～438
64. Kincho H Law and David R Mackay, Parallel row-oriented sparse solution method for finite element structural analysis, Inter. Jour. For Numer. Meth. In Engin., 1993,36:2895～2919
65．王思群，魏紫銮，Cholesky分解求解大型稀疏线性方程组的并行算法，数值计算与计算机应用，1996(2)：104～111
66．杜庆华等著，边界积分方程方法—边界元法．北京：高等教育出版社，1989
67. Das P C A, Disk-based block elimination technique used for the solution of nonsymmetrical fully populated matrix systems encountered in the boundary element method, In: C. A. Brebbia ed, Recent Advances in Boundary Element Methods, London: Pentech Press, 1978:391～404
68. M M Stabrowski, A block equation solver for large unsymmetric linear equation systems with dense coefficient matrices, Int. J. Numer. Methods Eng., 1987,24:289～300
69. M Rezayat, Fast decomposition of matrices generated by boundary element method, Int. J. Numer. Methods Eng., 1992,33:1109～1118
70．袁驷，边界元法中非对称满系数矩阵方程组的拟波阵解法及程序，计算结构力学及其应用，1986，3(1)：105～108
71．曹平，陈爱华，边界元法中线性方程组的拟波阵分块求解，计算力学学报，1999，16(1)：41～46
72. Lachat J C, Watson J O, Progress in the use of boundary integral equation illustrated by examples, Computer Methods in Applied Mechanics and Engineering, 1977,10:273～389
73. J M Cmtty, A block equation solver for large unsyrnmetric matrices arising in the boundary integral equation method, Int. J. Numer. Methods Eng., 1982,18:997-1017
74. R Bialecki, Linear equation solver for large block matrices arising in BEM, In: C A Brebbia, W L Wendland, G Kuhn ed, Boundary Element Ⅸ: Mathematical and Computational Aspects, Southampton: Computational Mechanics Publications, 1987:493～504
75. R H Rigby, M H Aliabadi, Out-of-core solver for large, multi-zone boundary element matrices, Int. J. Numer. Methods Eng., 1995,38:1507～1533
76. J H Kane, B L Kashava Kumar, Sunil Saigal, An arbitrary condensing, noncondensing solution strategy for large scale, multi-zone boundary element analysis, Computer Methods in Apllied Mechanics and Engineering, 1990,79:219～244
77. Ryszard A Bialecki, Markus Merkel, Horst Mews, Guther Kuhn, In- and out-of-core BEM equation solver with parallel and non-linear options, Int. J. Numer. Methods Eng., 1996,39: 4215～4242
78．吴旭光，徐汉忠，非均质问题的边界元不求逆的凝聚解法，河海大学学报，1994，22(2)：93～96
79．张效松，叶天麒，二维边界元奇异积分和多域缩聚法分析，计算力学学报，1997，14(2)：196～203
80．张效松，叶天麒，三维弹性力学边界元多域缩聚法分析，应用力学学报，1998，15(1)：16～22
81. F C Araujo, W J Mansur, Iterative solver for BEM systems of equations, In: C A Brebbia, J J Connor ed, Advances in Boundary Element: Computations and Fundamentals, Southampton: Computational Mechanics Publications, 1989, 263～274
82. F C Araujo, W J Mansur, J E B Malaghini, Biconjugate gradient acceleration for large BEM systems of equations, M Tanaka, C A Brebbia, T Honma ed, Boundary Element Ⅻ: Stress Analysis, Potential and Diffusion, Southampton: Computational Mechanics Publications, 1990: 99～110
83. F P Valente, H L G Pina, Iterative solvers for tridimensional BEM algebraic systems of equations, In: C A Brebbia, J B Martins, M H Aliabadi, N Haie ed, Boundary Element ⅩⅧ, Southampton: Computational Mechanics Publications, 1996:269～278
84. L P S Barra, W J Mansur, A L G A Coutinho, J C F Telles, Preconditioning techniques for iterative solutions of BEM systems of equations, In: C A Brebbia, J Dominguez, F Paris ed, Boundary Element ⅩⅣ Vol. 2: Stress Analysis and Computational Aspects, Southampton: Computational Mechanics Publications, 1992:643～650
85. C Y Leung, S P Walker, Iterative solution of large three-dimensional BEM elastostatic analyses using the GMRES technique, Int. J. Numer. Methods Eng., 1997,40:2227～2236
86. S Amini, N D Maines, Preconditioned krylov subspace methods for boundary element solution of the Helmholtz equation, Int. J. Numer. Methods Eng., 1996,41:875～898
87. N S Jovanovic, D E Keyes, K Guru Prasad, J H Kane, Drop tolerance ILU preconditioners for iterative solution techniques in boundary element analysis, In: C A Brebbia, J J Rencis ed, Boundary Element ⅩⅤ: Fluid Flow and Computational Aspects, Southampton: Computational Mechanics Publications, 1993:501～516
88．王人鹏，沈祖炎，钱若军，应用Krylov子空间方法求解边界元方程组，同济大学学报，1997，25(2)：212～217
89. J H Kane, D E Keyes, K Guru Prasad, Iterative solution techniques in boundary element analysis, Int. J. Numer. Methods Eng., 1991,31:1511～1536
90. K Guru Prasad, J H Kane, D E Keyes, C Balakrishna, Preconditioned krylov solvers for BEA, Int.
J. Numer. Methods Eng., 1994,37:1651～1672
91. F C de Araujo, G J Belmonte, M S R Freitas, On the use of iterative solvers for generating efficient 3D multidomain boundary element algorithms, In: C A Brebbia, H Power ed. Boundary Element ⅩⅪ, Southampton: WIT Press, 1999:219～228
92. N S Jovanovic, D E Keyes, K Guru Prasad, J H Kane, Drop tolerance ILU preconditioners for iterative solution techniques in boundary element analysis, In: C A Brebbia, J J Rencis ed, Boundary Element ⅩⅤ: Fluid Flow and Computational Aspects, Southampton: Computational Mechanics Publications, 1993:501～516
93. T J Urekew, J J Rencis, A hybrid equation solver for BEM, In: C A Brebbia, J J Rencis ed, Boundary Element ⅩⅤ: Fluid Flow and Computational Aspects, Southampton: Computational Mechanics Publications, 1993:529～549
94. Symm G T, Boundary elements on a distributed army processor, Engineering Analysis, 1984,1: 162～165
95. Davies A J, The boundary element method on the ICL DAP, Parallel Computing, 1988,8: 348～353
96. A J Davies, The boundary element method on a transputer network, In: C A Brebbia, G S Gipson ed, Boundary Element ⅩⅢ, Southampton: Computational Mechanics Publications, 1991: 985～994
97. Alberto Zucchini, Subrata Mukherjee, Vectorial and parallel processing in stress analysis with the boundary element method, Int. J. Numer. Methods Eng., 1991,31: 307～317
98. J M Cela, A Julia, High performance computing on boundary element simulations, In: C A Brebbia, H Power ed, Boundary Element ⅩⅫ, Southampton: WIT Press, 2000:175～179
99. A J Davies, A parallel implementation of the dual reciprocity boundary element method, In: C A Brebbia, J Dominguez, F Paris ed, Boundary Element ⅩⅧ Vol. 2: Stress Analysis and Computational Aspects, Southampton: Computational Mechanics Publications, 1992:613～626
100．尹欣，姚振汉，程建钢，基于微机机群网络的边界元并行计算，重庆建筑大学学报，2000，22(6)：92～95
101．姚振汉，蒲军平，尹欣，段小华，边界元法应用的若干近期研究，力学季刊，2001，22(1)：10～17
102. M S Ingber, D E Womble, A parallel iterative equation solver for the analysis of suspension flows using the boundary element method, In: M Marchetti, C A Brebbia, M H Aliabadi ed, Boundary Element ⅩⅠⅩ, Southampton: Computational Mechanics Publications, 1997:583～592
103. K A Kline, N K Tsao, C B Friedlander, Parallel processing and the solution of boundary element equations, In: T A Cruse, A B Pifko, H Armen ed, Advanced Topic In Boundary Element Analysis, New York: The American Society of Mechanical Engineers, 1985:257～270
104. N Kamiya, H Iwase, E Kita, Parallel algorithm for BEM analysis, In: C A Brebbia, J B Martins, M H Aliabadi, N Haie ed, Boundary Element ⅩⅧ, Southampton: Computational Mechanics Publications, 1996:163～171
105. N Kamiya, H Iwase, Boundary element domain decomposition method and its parallelization for the problem exhibiting nonlinear boundary conditions, In: M. Marchetti, C A Brebbia, M H Aliabadi ed, Boundary Element ⅩⅠⅩ, Southampton: Computational Mechanics Publications, 1997:573～582
106. D Crann, A J Davies and J Mushtaq, Parallel Laplace transform boundary element methods for diffusion problem, In: A Kassab, C A Brebbia, M Chopin ed, Boundary Element ⅩⅩ, Southampton: Computational Mechanics Publications, 1998:259～268
107. A J Davies, D Crann, J Mushtaq, A parallel implementation of the Laplace transform BEM, In: C A Brebbia, J B Martins, M H Aliabadi, N Haie ed, Boundary Element ⅩⅧ, Southampton: Computational Mechanics Publications, 1996:163～171
108. C Catlett, L Smarr, Metacomputing, Comm. of ACM, 1992,35(6): 44～52
109. T E Anderson, D E Culler, D A Patterson et al, A case for NOW(Networks of Workstations), IEEE Micro, 1995,(4): 54～64
110. C Amza, A L Cox, S D Warkadas et al, TreadMarks: Shared memory computing on networks of workstations, IEEE Computer, 1996,29(2): 18～28
111．戴光明，戴晓明，基于PVM的微机网络并行计算及其应用，计算机工程与应用，2000，(9)：154～156
112．王莹，屈一新，PC集群的建立与MPI并行环境的实现及其应用，北京化工大学学报，2001，28(4)：4～6
113．黎康保，陶文正等，用PC机群组构并行超级计算机，计算机工程，2000，26(9)：1～3
114．岳光来，杨耀忠等，局域网分布式并行计算环境的建立与应用，计算机工程与应用，2002，(4)：136-138
115．张效松，叶天麒，葛守廉，边界积分方程—非连续边界元离散方法及其应用，计算力学学报，2001，18(3)：331～334
116．杜庆华等著，边界积分方程方法——边界元法，北京：高等教育出版社，1989
117．C．A．布瑞比亚等著，边界单元法的理论和工程应用，北京：国防工业出版社，1988
118．Cao Zhihao，Chen Guangxi，Hou Xiaodong,A convergent restarted GMRES algorithm，复旦大学学报(自然科学版)，1997，36(6)：645～651
119. L Wang, A. Semlyen, Applacation of sparse eigenvalue techniques to the small signal stability analysis of large power systems, IEEE Trans. Power Systems, 1990(5): 635～642
120. J W Daniel, W B Gragg, L Kattfinan, G W Stewart, Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factodzafion, Mathematics of Computation, 1976,30(136): 772～795
121．G．D马诺利斯，D E贝斯科思，弹性动力的边界元法，天津：天津科学技术出版社，1991
122. George D Manolis, A comparative study on three boundary element method approaches to problems in elastodynamies, Int. J. Numer. Methods Eng., 1983,19:73～91
123．王有成编，工程中的边界元方法，北京：中国水利水电出版社，1996