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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.
The eigenvalue calculation of symmetric matrix tridiagonalization and tridiagonal symmetric matrix is the key step of the parallel solver for dense symmetric matrix features.For the multi-level architecture of SMP cluster system, the matrix tridiagonalization based on Householder transform and the tris The algorithm of divide and conquer for the eigenvalue problem of diagonal matrix is given and their MPI + OpenMP hybrid parallel algorithms are given.The algorithm focuses on load balancing, communication overhead and performance evaluation in the SMP cluster system environment.The hybrid parallel algorithm is designed with coarse-grained Thread parallel mode and task invocation dynamically invoke method to improve the load balancing problem in MPI algorithm and reduce the communication overhead.Experiments on Deepeng 6800 show that the solver based on hybrid parallel algorithm has more advantages than pure MPI version solver Better performance and scalability.