Solving finite element equations on concurrent computers
Solving finite element equations on concurrent computers
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DOI：
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发表时间：
1987
影响因子：
3.9
通讯作者：
B. Nour-Omid;A. Raefsky;G. Lyzenga
中科院分区：
文献类型：
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作者：
B. Nour-Omid;A. Raefsky;G. Lyzenga
本文讨论了用于求解有限元应用中出现的方程组的并发算法的开发。该方法基于直接消除法和预条件共轭迭代的混合。使用两种不同的预处理器；对角缩放和不完全 LU 分解的并发实现。首先，使用自动程序将有限元网格划分为子结构。选择特定的网格分区以最小化在并发计算机上使用该算法评估解决方案的成本估计。这些程序在 JPL/CalTech MARK III 超立方计算机上的有限元程序中实现。概述了该程序的结构。借助大量数值测试运行证明了该求解方法的性能，并讨论了其并发实现的优点。重点介绍了数值示例中顺序机器的效率和加速因素。
This paper discusses the development of a concurrent algorithm for the solution of systems of equations arising in finite element applications. The approach is based on a hybrid of direct elimination method and preconditioned conjugate iteration. Two different preconditioners are used; diagonal scaling and a concurrent implementation of incomplete LU factorization. First, an automatic procedure is used to partition the finite element mesh into sub-structures. The particular mesh partition is chosen to minimize an estimate of the cost for evaluating the solution using this algorithm on a concurrent computer. These procedures are implemented in a finite element program on the JPL/CalTech MARK III hypercube computer. An overview of the structure of this program is presented. The performance of the solution method is demonstrated with the aid of a number of numerical test runs, and its advantages for concurrent implementations are discussed. Efficiency and speed-up factors over sequential machines for the numerical examples are highlighted.