arXiv 2103.050342021-03-08hep-lat

畴壁费米子多重网格方法的比较

Comparison of Domain Wall Fermion Multigrid Methods

Peter Boyle, Azusa Yamaguchi

摘要：

我们提出了一个详细的比较最近和新的几种方法，多重网格求解算法适合于解决5D手性费米子行动，如域壁费米子在沙米尔制定，也为部分分数和连续分数重叠。我们的重点是加速规范配置采样，并需要一个紧凑的最近邻模板，以限制获得一个粗略的运营商的计算成本。这需要一个最近的邻居运营商的粗化，以保持稀疏粗化网格，不像HDCG。我们比较了HDCR和多重网格算法的方法以及几种新的混合方案。在这项工作中，我们介绍了一个新的递归切比雪夫多项式为基础的设置计划。我们发现，HDCR的方法，可以设置，并解决标准沙米尔域壁费米子比一个单一的解决与红黑预处理共轭共轭体的大容量和现代GPU系统，如首脑会议超级计算机。这对于加速HMC是有希望的，特别是如果设置成本在多个Hasenbusch决定性因素之间分摊。该设置方案可能普遍适用于其他费米子作用。

英文摘要：

We present a detailed comparison of several recent and new approaches to multigrid solver algorithms suitable for the solution of 5d chiral fermion actions such as Domain Wall fermions in the Shamir formulation, and also for the Partial Fraction and Continued Fraction overlap. Our focus is on the acceleration of gauge configuration sampling, and a compact nearest neighbour stencil is required to limit the calculational cost of obtaining a coarse operator. This necessitates the coarsening of a nearest neighbour operator to preserve sparsity in coarsened grids, unlike HDCG. We compare the approaches of HDCR and the Multigrid algorithm and also several new hybrid schemes. In this work we introduce a new recursive Chebyshev polynomial based setup scheme. We find that the HDCR approach, can both setup, and solve standard Shamir Domain Wall Fermions faster than a single solve with red-black preconditioned Conjugate Gradients on large volumes and for modern GPU systems such as the Summit supercomputer. This is promising for the acceleration of HMC, particularly if setup costs are shared across multiple Hasenbusch determinant factors. The setup scheme is likely generally applicable to other Fermion actions.

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