【作者】 张健飞；

【导师】 姜弘道；

【作者基本信息】 河海大学 ， 水工结构工程， 2004， 博士

【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。更多还原

【Abstract】 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-domainas 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更多还原