有限元并行计算的MPI程序设计  

MPI Programming for Parallel Computing of Finite Element Method

作　　者：雒战平[1] 刘之行[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《西安交通大学学报》2004年第8期873-876,共4页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(10371095).

摘　　要：以Poisson方程边值问题的求解为背景,实现了有限元并行计算的MPI程序设计.通过生成一种特殊结构的刚度矩阵,并在此基础上,设计了一套有效的并行计算策略,使计算的并行性得到很好的开拓,实现了包括刚度矩阵的生成、刚度矩阵的三角分解以及解三角方程组的并行执行.程序在国家高性能计算中心(西安)的曙光3000上进行了数值试验,结果表明,随着开辟进程数目的增多,加速比变得比较理想,当进程数目为30时,表明该进程数目在最优进程值附近.在60台处理器(进程)上计算18万个节点的大规模问题时,共耗时176 96415s.Taking solving Poisson boundary problem as a sample, an MPI programming for parallel computing of finite element method is completed. On the basis of generating a kind of stiffness matrix with special structure, a task assignment is proposed to implement parallelly constructing the stiffness matrix, computing the LDLT factors and solving the triangular systems. Some numerical experiments carried out on the high performance computer SHUGUANG 3000 indicate that higher efficiency can be obtained as the number of processor increases, and the optimized number approaches to 30. It takes less than 3 minutes when the problem is with 180000 nodes.

关 键 词：并行计算 分布式存储 数据结构 有限元方法 MPI编程 

分 类 号：O242.21[理学—计算数学]