初边值问题的块三对角可扩展并行算法  

Scalable Parallel Algorithm of Block Tridiagonal Systems for Initial Boundary Value Problem

作　　者：张武[1] 张衡[1] 

机构地区：[1]上海大学计算机工程与科学学院,上海200072

出　　处：《上海大学学报（自然科学版）》2007年第5期497-503,共7页Journal of Shanghai University:Natural Science Edition

基　　金：教育部科学技术研究重点项目(205051);上海市自然科学基金资助项目(05ZR14050)

摘　　要：该文对二维抛物型方程带Dirichlet边界条件初边值问题的离散系统使用块三对角可扩展并行算法求解.提出反映差分格式内在并行性的概念——差分格式的并行度,利用这个概念说明差分格式自身内在并行性对并行算法性能的影响.使用该方法在上海大学超级计算机"自强3000"上进行了数值实验,实验结果与理论分析一致.在保证精度的前提下,得到线性加速比,并行效率达到90%以上.A scalable parallel algorithm of block tridiagonal systems is discussed to solve initial boundary value problems of 2D-parabolic equation with the Dirichlet boundary condition. A parallel degree of the difference scheme is proposed to show the intrinsic parallelism of the difference scheme. The relation between the parallel degree and the performance of the parallel algorithm is investigated. The proposed method has been implemented on the supercomputer ＂ZiQiang 3000＂ of Shanghai University. The numerical results closely match the theoretical analysis. At given accuracy, the linear speedup rate is obtained, and parallel efficiency over 90% is reached.

关 键 词：块三对角线性方程组 块对角占优 并行度 矩阵分割 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]