结构动力分析隐式积分并行算法与实现

Parallel algorithms for dynamics analysis of structures and their impementations

在分布式并行计算机环境下进行了有限元并行算法的研究，建立了结构动力分析的两种隐式积分方法（Ｎｅｗｍａｒｋ方法和Ｗｉｌｓｏｎ－θ方法）的并行化方法与算法步骤，设计了变带宽一维存储时有效刚度矩阵的三角分解并行算法；基于Ｔｒａｎｓｐｕｔｅｒ的分布式ＭＩＭＤ并行计算机上，采用３Ｌ并行ＦＯＲＴＲＡＮ编写了计算程序，并将其移植到有限元串并行混合分析软件ＰＦＥＭ中。以平面问题和空间板弯问题作为实例进行了数值计算。结果表明计算方法具有较高的并行效率。当自由度为７５７９，最大带宽为７２６时，２个和３个处理器工作的并行效率分别为０．７０和０．５５。

The parallel algorithms for FEM in the distributed memory environment are studied. Two implicit parallel time integration algorithms are presented, which are, respectively, the paralleled Newmark method and Wilsion θ method. Emphasis is placed on the parallel LDL T decomposition of the equivalent stiffness matrices in the two methods. The algorithms are carried out in the MIMD environment on Transputer, and are also integrated into the available PFEM package which is a serial parallel mixed FEM softward. As verifying examples, a plane problem in elasticity and a 3D plate problem are presented. The result shows that the parallel efficiencies in present method are satisfactory as well, which are 0.70 and 0.55 respectively when the degree of freedom (DOF) is 7579, and the maximum bandwidth is 726 under two processors and three processors.