摘要
精确对角化(exact diagonalization)方法是一种在量子物理、凝聚态物理等领域广泛应用的数值计算方法,是最直接求得量子系统基态的数值方法.仅从哈密顿矩阵的对称性出发,利用无矩阵(matrix-free)方法、分层通信模型以及适配于MT-3000的数据级并行算法,提出了面向天河新一代超算系统上的超大稀疏哈密顿矩阵向量乘异构并行算法,可以实现基于一维Hubbard模型的大规模精确对角化.提出的并行算法在天河新一代超算系统上进行了测试,其中在1400亿维度矩阵规模上,8192进程相比256进程强扩展效率为55.27%,而弱扩展到7300亿维度矩阵规模上,13740个进程相比64进程的弱扩展效率保持在51.25%以上.
The exact diagonalization(ED)method,a key numerical technique in quantum and condensed matter physics,directly computes the ground state of quantum systems.This study leverages Hamiltonian matrix symmetry,matrix-free methods,hierarchical communication models,and a data-level parallel algorithm optimized for the MT-3000 architecture.We propose a heterogeneous parallel algorithm for large-scale sparse Hamiltonian matrix-vector multiplication on the new generation Tianhe supercomputing system,enabling large-scale exact diagonalization for the one-dimensional Hubbard model.Tests on the Tianhe new generation system show a strong scaling efficiency of 55.27% when scaling from 256 to 8192 processes for a 140-billion-dimension matrix.Weak scaling efficiency remains above 51.25% when scaling from 64 to 13740 processes for a 730-billion-dimension matrix.
作者
李彪
刘杰
王庆林
Li Biao;Liu Jie;Wang Qinglin(Laboratory of Digitizing Software for Frontier Equipment(National University of Defense Technology),Changsha 410073;National Key Laboratory of Parallel and Distributed Computing(National University of Defense Technology),Changsha 410073;College of Computer Science and Technology,National University of Defense Technology,Changsha 410073)
出处
《计算机研究与发展》
北大核心
2025年第6期1347-1362,共16页
Journal of Computer Research and Development
基金
国家重点研发计划项目(2023YFA1011704,2021YFBO300101)。
