混凝土静动力学分析数值模拟程序中的并行算法设计

对混凝土进行静动力学分析的数值模拟程序，从多个方面考虑了其中的并行算法设计。首先，从整体上提出了一个将有限单元分布与未知量分布有机结合的整体并行算法设计方案。之后，分别针对刚度矩阵装配、双门槛不完全Cholesky分解预条件、稀疏矩阵与向量相乘、稀疏向量相加等核心算法，提出了相应的高效并行算法。在由8台奔腾4微机组成的机群上对一采用 44117个网格点与53200个有限单元的混凝土断裂过程数值模拟表明，加速比可以达到6.92，与单机算法改进效果相结合后，一次加载的计算时间从原程序的11443s减少到了13s。在有4个CPU的一台Sun HPC上对采用71013个网格点与78800个有限单元的问题进行数值模拟时，串行算法改进与并行算法的设计也使得整个过程所需的计算时间从原串行程序的约15d减少到只要122min。

Application of parallel computing technique in programming of numerical simulation for concrete under static-dynamic load

The parallel computing technique is applied to design the programming for numerical simulating the fracture and damage of concrete under static-dynamic load. First, the overall framework for the parallel computation of the combination of finite element distribution with unknown quantity distribution is established. The whole computation is based on FEM. Consequently, the high efficiency parallel computation is realized by introducing the assembly process of the stiff matrix, incomplete Cholesky factorization with double threshold, multiplication of a sparse matrix with a vector and two sparse vectors. By means of this technique the computation speed on a cluster with 8 Pentium 4 personal computers for simulating the fracture process of a concrete block with 441117 grids and 53200 elements is accelerated by 6.92 times. Comparing with the original computation method the time spent to simulate the one step of loading reduced from 11443 sec. To 13 sec. On a Sun workstation with 4 processors, the computation for simulating the fracture of a concrete block with 71013 discrete points and 78800 finite elements the computation time consumption is reduced from 15d. to 2hr. The advantage of parallel Computing technique is remarkable.