三维抛物型初边值问题的块三对角可扩展并行算法  

A Scalable Parallel Algorithm of Block Tridiagonal Systems for the Initial Boundary Value Problem of 3D-Parabolic Equation

作　　者：张衡[1] 张武[1] 

机构地区：[1]上海大学计算机工程与科学学院

出　　处：《微电子学与计算机》2007年第9期16-18,共3页Microelectronics & Computer

基　　金：2005年度教育部科学技术研究重点项目(205051);2005年上海市自然科学基金项目(05ZR14050)

摘　　要：对三维抛物型方程带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。提出了反映差分格式内在并行性的概念——差分格式的并行度,讨论了差分格式的并行度与并行算法性能的关系。使用此方法在上海大学超级计算机"自强3000"上进行了数值实验,实验的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 for solving the initial boundary value problem of 3D-parabolic equation with the Dirichlet boundary condition is discussed. A parallel degree of the difference scheme is proposed for showing its intrinsic parallelism of the difference scheme. The relation between the parallel degree and the performance of the parallel algorithm is investigated. The method proposed in this paper has been implemented on the super computer ＂ZiQiang 3000＂ of Shanghai University, and the numerical results match closely with theoretical analysis. With the given accuracy, the line speedup is obtained, and the parallel implementation efficiency over 90% is reached.

关 键 词：块三对角线性方程组 块对角占优 差分格式 并行度 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]