一种基于随机抽样的新型HSS结构多波前求解器的高效多核实现
An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling
摘要：
我们提出了一个稀疏的线性系统求解器，是基于高斯消除的多波前变体，并利用低秩近似的密集的前端矩阵。我们使用层次半可分（HSS）矩阵，其中有低秩非对角块，近似的正面矩阵。对于HSS矩阵构造，随机采样算法与插值分解一起使用。随机化压缩与快速ULV HSS分解的组合导致求解器具有比许多应用的标准多波前方法更低的计算复杂性，导致在我们的测试套件中的问题的加速高达7倍。该实现通过使用具有动态运行时调度的任务并行性来针对众核系统。数值实验表明，性能的改善，国家的最先进的稀疏直接求解器。该实现在一系列现代共享内存并行系统（包括英特尔至强融核（MIC））上实现了高性能和良好的可扩展性。该代码是一个软件包的一部分，称为STRUMPACK --矩阵压缩包，它也有一个分布式存储器组件的密集秩结构矩阵。
英文摘要：
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factorization leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK -- STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.
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