块三对角线性方程组的一类二维区域分解并行不完全分解预条件  

Parallel Incomplete Factorization Preconditioning of Block Tridiagonal Linear Systems with 2-D Domain Decomposition

作　　者：吴建平[1] 宋君强[1] 张卫民[1] 李晓梅[2] 

机构地区：[1]国防科技大学计算机学院,湖南长沙410073 [2]装备指挥技术学院,北京101416

出　　处：《计算物理》2009年第2期191-199,共9页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(60803039,40505023);北京应用物理与计算数学研究所计算物理实验室基金、并行与分布处理国家重点实验室基金资助项目

摘　　要：基于二维重叠区域分解,对每个子区域上局部不完全LU分解所得到的上、下三角因子分别进行组合,给出一类全局并行不完全分解型预条件.所给出的并行化方法适用于任何不完全LU分解型预条件.对采用二维区域分解与一维区域分解时所得并行预条件的并行计算性能进行分析比较.实验结果表明,提出的并行化方法普遍优于加性Schwarz并行化方法,且当处理器个数相对较多时采用二维区域分解优于一维区域分解.Based on two-dimensional domain decomposition with small overlapping, we provide a method in which local lower and upper triangular incomplete factors are combined into an effective approximation for global incomplete lower and upper triangular factors of coefficient matrix. Parallelization method is applicable to any preconditioner of incomplete type. Parallel performance metric of two-dimensional parallel preeonditioner is compared to that of one-dimensional ones. Experiments show that it is more efficient than additive Sehwarz technique and twodimensional decomposition is better than corresponding one-dimensional decomposition as more processors are used for parallel computation.

关 键 词：线性方程组求解 块三对角矩阵 不完全分解 加性Schwarz 并行算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]