摘要
该文讨论了一类求解大规模非线性方程组算法的并行性能及其在曙光并行机上的实现过程 .与传统的算法不同之处是用一个块对角矩阵作为迭代矩阵 ,且该矩阵可由一个仅包含向量内积和矩阵与向量乘积的递推关系简便计算得到 .在对算法进行描述之后 ,分析了算法的并行加速比和存储需求 ,讨论了算法在基于消息传递的 MPI并行环境下的实现流程 ,数值计算表明理论分析与数值结果相符合 ,算法在分布式并行环境下具有较好的并行度和较低的存储要求 。
This paper discusses parallelism of algorithms for solving large-scale nonlinear systems of equations. The basic idea is to replace the Jacobian matrix in a Newton algorithm by a block-diagonal Broyden matrix, which can easily be updated by a recurrence relation. Combining it with some iterative or direct linear solvers, it is possible to obtain a family of nonlinear solvers. The nonlinear system arises from Bratu problem by a finite difference method. Pseudcode of the algorithm using MPI in C language is presented. Several tests are performed in varying sizes of the systems and block numbers in order to study the advantages and weaknesses of such a method. Numerical results show that the algorithms are effective, and that they can be used in the large scale problems arising from scientific and engineering computing. In future work, it is intended to apply some parallelizable preconditioning techniques to the BB-methods (for example, SSOR or block parallelizable ILU(0) preconditioners) in order to accelerate the convergence of such methods, and also to increase their robustness.
出处
《计算机学报》
EI
CSCD
北大核心
2002年第4期397-402,共6页
Chinese Journal of Computers
基金
教育部留学回国人员科研启动基金
国家高性能计算基金 (9912 7)资助
