The evaluation of Fock exchange is often the computationally most expensive part of hybrid functional density functional theory calculations in a systematically improvable, complete basis. In this work, we employ a Tucker tensor based approach that substantially accelerates the evaluation of the action of Fock exchange by transforming three-dimensional convolutional integrals into a tensor product of one-dimensional convolution integrals. Our numerical implementation uses a parallelization strategy that balances the memory and communication bottlenecks, alongside overlapping compute and communication operations to enhance computational efficiency and parallel scalability. The accuracy and computational efficiency are demonstrated on various systems, including Pt clusters of various sizes and a TiO₂ cluster with 3684 electrons.

中文翻译：

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塔克张量方法用于加速广义 Kohn-Sham 密度泛函理论实空间有限元离散中的 Fock 交换计算

在系统可改进的、完整的基础上，Fock 交换的评估通常是混合泛函密度泛函理论计算中计算成本最高的部分。在这项工作中，我们采用基于 Tucker 张量的方法，通过将三维卷积积分转换为一维卷积积分的张量积，大大加速了 Fock 交换行为的评估。我们的数值实现使用并行化策略来平衡内存和通信瓶颈，以及重叠的计算和通信操作，以提高计算效率和并行可扩展性。准确性和计算效率在各种系统上得到了证明，包括各种尺寸的 Pt 簇和具有 3684 个电子的 TiO ₂簇。