求解大型线性方程组的通信隐藏流水线BiCGSafe方法
Communication-hiding pipelined BiCGSafe methods for solving large linear systems
摘要：
最近，已经提出了BiCGStab方法的新变体，称为管道BiCGStab。该方法可以通过一种机制来实现更高程度的可扩展性和加速率，在该机制中，用于计算内积的通信阶段可以与矩阵-向量积的计算重叠。另一方面，存在几种比BiCGStab具有更好收敛行为的广义迭代方法，例如ssBiCGSafe，BiCGSafe，GPBi-CG。在这些方法中，ssBiCGSafe，它需要一个单一的阶段计算每一个迭代的内积，是最适合于高性能计算系统。在本文中，灵感的成功的流水线BiCGStab方法，我们提出了变化的ssBiCGSafe方法，其中只有一个阶段的内积计算每次迭代是必需的，这个内积计算阶段可以重叠的矩阵向量计算。通过数值实验，我们表明，所提出的方法导致改善的收敛行为和执行时间相比，流水线的BiCGStab和ssBiCGSafe方法。
英文摘要：
Recently, a new variant of the BiCGStab method, known as the pipeline BiCGStab, has been proposed. This method can achieve a higher degree of scalability and speed-up rates through a mechanism in which the communication phase for the computation of the inner product can be overlapped with the computation of the matrix-vector product. On the other hand, there exist several generalized iteration methods with better convergence behavior than BiCGStab such as ssBiCGSafe, BiCGSafe, GPBi-CG. Of these methods, ssBiCGSafe, which requires a single phase of computing inner products per one iteration, is best suited for high-performance computing systems. In this paper, inspired by the success of the pipelined BiCGStab method, we propose variations of the ssBiCGSafe method, in which only one phase of inner product computation per iteration is required and this inner product computation phase can be overlapped with the matrix-vector computation. Through numerical experiments, we show that the proposed methods lead to improvements in convergence behavior and execution time compared to the pipelined BiCGStab and ssBiCGSafe methods.
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