Analysis of Numerical Simulation of Tunnel Excavation Based on High Performance Parallel Finite Element Computing
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摘要: 随着岩土工程规模的不断扩大、复杂性的增加以及计算参数的多样化和计算精度的提高, 人们对于计算机计算能力的要求越来越高, 然而单处理器无法满足这类大规模计算.从数据输入、区域分解、线性方程组的迭代求解、后处理等方面详细阐述高性能计算平台上并行有限元求解大规模岩土工程的关键问题.提出了利用MPI2的新特性进行海量数据的分段并行读入, 采用ParMetis软件并行地进行区域分解, 实现了前处理过程的完全并行化; 采用基于Jacobi预处理技术的预处理共轭梯度法(PCG)进行线性方程组的并行迭代求解; 采用Paraview软件实现了后处理的并行可视化.在深腾7000系统上对某隧道工程的三维开挖过程进行了数值模拟, 对其并行性能进行了分析和评价, 验证了采用的区域分解算法和系统方程组的求解方法的可行性, 并且具有较高的加速比和并行效率.Abstract: With the expansion of the scale of geotechnical engineering, the increase of the complexity and diversity of the calculation parameters and the improvement of calculation accuracy, the requirement of computer computing power is higher, but a single processor can't meet this kind of large-scale computing.Key issues involving the data input, domain decomposition technique, iteration solution algorithm of linear system, and post processing for large scale geotechnical engineering using parallel finite element method based on high performance computation platform are presented in this paper. The study includes a case analysis of a tunnel evacuation in the following procedure. A new feature was employed so that massive data can be read in parallel, and parallel software, i.e. ParMetis was used to decompose the domain, then the pre-process was in completely parallel. The preconditioned conjugate gradient method based on Jacobi preconditioner was applied to solve linear system. In post processing, the parallel visual model was obtained through the Paraview software. A 3D tunnel excavation was simulated in DeepComp 7000 system, on basis of which the parallel performance is analyzed and evaluated, Verified by domain decomposition algorithm and the feasibility of the method of solving the system equations, and has high speedup ratio and parallel efficiency.
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图 3 并行加速比(a)和并行加速效率(b)
Fig. 3. Parallel speedup (a) and parallel efficiency (b) of variable number of processors
表 1 隧道围岩和衬砌的物理力学指标
Table 1. Comparison between initial stresses and stresses got in the back analysis
材料 密度(kN·m-3) 弹性模量(GPa) 泊松比 摩擦角(°) 膨胀角(°) 粘聚力(MPa) Ⅲ级围岩 24 15 0.28 45 15 1.4 Ⅳ级围岩 20 4 0.31 35 20 0.7 衬砌 25 30 0.20 - - - 
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表 2 方程组迭代求解次数和时间
Table 2. Iteration number and computation time of equations
预处理技术 处理器个数 迭代次数 求解时间(s) 无预处理 1 1 112 136.70 8 1 096 580.56 64 1 112 9.84 Jacobi预处理 1 425 30.20 8 422 175.71 64 411 3.73
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表 3 程序各部分的计算时间
Table 3. The computing time of various parts of the program
并行程序计算过程 76 917个单元 247 434个单元 1 081 879个单元 时间(s) 比重(%) 时间(s) 比重(%) 时间(s) 比重(%) 网格读取及子区域划分 2.70 2.7 7.59 5.7 15.02 1.8 子区域刚度及荷载计算 7.41 7.3 9.88 7.4 136.01 15.9 系统方程组的迭代求解 90.16 88.6 112.56 84.5 696.80 81.5 后处理 1.51 1.4 3.20 2.4 6.73 0.8 总计 101.78 100.0 133.23 100.0 854.46 100.0
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表 4 不同处理器数目的计算时间
Table 4. The computing time of variable number of processors
处理器数 系统方程组求解时间(s) 总计算时间(s) 76 917单元 247 434单元 1 081 879单元 76 917单元 247 434单元 1 081 879单元 1 775.50 983.90 6 715.70 863.20 1 198.00 7 910.90 8 150.40 180.20 1 112.20 157.20 195.50 1 209.40 16 90.16 112.56 696.80 101.78 133.23 854.46 32 50.71 65.64 380.63 52.43 74.32 453.57 64 30.59 40.67 230.63 31.35 42.65 270.21 80 24.18 36.25 200.72 27.51 37.19 234.54
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