Abstract We present an efficient implementation of polynomial filtering methods in PARSEC, a real-space pseudopotential based Kohn–Sham density functional theory solver. The implementation described here improves upon a Chebyshev-filtered subspace iteration algorithm used in the previous version of PARSEC. We present a hybrid polynomial filtering scheme that combines Chebyshev-filtered subspace iteration and a spectrum slicing method that partitions the spectrum into several spectral slices and uses bandpass-filtered subspace iteration to compute approximate eigenpairs within each interior slice simultaneously. We describe a procedure to partition a spectrum and construct polynomial filters. We also discuss a number of practical issues such as the use of appropriate data layouts for carrying out the computation on a two-dimensional process grid and how to achieve good load balance by allocating an appropriate number of process groups to each spectral slice. Numerical examples are presented to demonstrate the effectiveness of the hybrid polynomial filtering method as well as the superior parallel scalability of spectrum slicing in comparison to that of Chebyshev-filtered subspace iteration.

中文翻译：

---

PARSEC 中密度泛函理论计算多项式滤波的可扩展实现

摘要 我们提出了 PARSEC 中多项式滤波方法的有效实现，PARSEC 是一种基于实空间赝势的 Kohn-Sham 密度泛函理论求解器。此处描述的实现改进了先前版本的 PARSEC 中使用的切比雪夫过滤子空间迭代算法。我们提出了一种混合多项式滤波方案，该方案结合了切比雪夫滤波子空间迭代和频谱切片方法，该方法将频谱划分为几个频谱切片，并使用带通滤波子空间迭代同时计算每个内部切片内的近似特征对。我们描述了一个划分频谱和构建多项式滤波器的过程。我们还讨论了许多实际问题，例如使用适当的数据布局在二维过程网格上执行计算，以及如何通过为每个光谱切片分配适当数量的过程组来实现良好的负载平衡。数值例子证明了混合多项式滤波方法的有效性以及与切比雪夫滤波子空间迭代相比，频谱切片的优越并行可扩展性。