低通信高性能从头算密度矩阵重整化群算法
Low communication high performance ab initio density matrix renormalization group algorithms
摘要：
最近，在高性能计算平台上部署从头计算密度矩阵重整化群计算引起了人们的兴趣。在这里，我们介绍了传统的分布式内存从头DMRG算法，将其连接到概念上更简单和有利的子哈密尔顿方法的总和的重新制定。从这个框架开始，我们进一步探讨了一个层次的并行策略，其中包括（i）子哈密尔顿算子的总和上的并行，（ii）在网站上的并行，（iii）在正常和互补运算符上的并行，（iv）在对称扇区上的并行，以及（v）在密集矩阵乘法上的并行。我们描述了如何减少处理器负载不平衡和通信成本的算法，以实现更高的效率。我们说明了我们的新的开源实现的性能在最近的基准基态计算苯的轨道空间的108个轨道和30个电子，键的尺寸高达6000，和模型的FeMo辅因子与76个轨道和113个电子。从448到2800个CPU核心的并行扩展几乎是理想的。
英文摘要：
There has been recent interest in the deployment of ab initio density matrix renormalization group computations on high performance computing platforms. Here, we introduce a reformulation of the conventional distributed memory ab initio DMRG algorithm that connects it to the conceptually simpler and advantageous sum of sub-Hamiltonians approach. Starting from this framework, we further explore a hierarchy of parallelism strategies, that includes (i) parallelism over the sum of sub-Hamiltonians, (ii) parallelism over sites, (iii) parallelism over normal and complementary operators, (iv) parallelism over symmetry sectors, and (v) parallelism over dense matrix multiplications. We describe how to reduce processor load imbalance and the communication cost of the algorithm to achieve higher efficiencies. We illustrate the performance of our new open-source implementation on a recent benchmark ground-state calculation of benzene in an orbital space of 108 orbitals and 30 electrons, with a bond dimension of up to 6000, and a model of the FeMo cofactor with 76 orbitals and 113 electrons. The observed parallel scaling from 448 to 2800 CPU cores is nearly ideal.
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