SMP集群系统上矩阵特征问题并行求解器的有效算法

对称矩阵三对角化和三对角对称矩阵的特征值求解是稠密对称矩阵特征问题并行求解器的关键步 .针对SMP集群系统的多级体系结构,基于Householder变换的矩阵三对角化和三对角矩阵特征值问题的分而治之算法,给出了它们的MPI OpenMP混合并行算法 .算法研究集中在SMP集群系统环境下的负载平衡、通信开销和性能评价 .混合并行算法的设计结合了粗粒度线程并行模式和任务共享的动态调用方法,改善了MPI算法中的负载平衡问题、降低了通信开销 .在深腾6800上的实验表明,基于混合并行算法的求解器比纯MPI版本的求解器具有更好的性能和可扩展性 .

Efficient Algorithms for Matrix Eigenproblem Solver on SMP Cluster

Tridiagonalization of symmetric matrices and computing eigenvalues of tridiagonal symmetric matrix are the keys of eigenproblem parallel solver of dense symmetric matrix. Aimed at the memory hierarchy of the SMP cluster and based on both matrix tridiagonalization using Householder transform and divide-and-conquer algorithm for tridiagonal eigenproblem, their MPI OpenMP hybrid parallel implementations are presented. These studies focus on load balance, communication overhead and performance evaluation on the SMP cluster. Hybrid parallel algorithm design combines the coarse-grain model and dynamic task sharing, thus resolving the load balance problem and decreasing the communication overhead in MPI parallel algorithm. It is shown from the tests on Deepcomp 6800 that the parallel solver based on hybrid parallel implementation has better performance and scalability than that based on pure MPI implementation.