密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度，在应用于二维或准二维问题时，要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略，可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分，实现了数据的分布式存储，并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例，测试了异构并行程序在不同DMRG保留状态数下的运行表现，并给出了相应的性能基准.应用于4腿梯子时，观测到了高温超导中常见的电荷密度条纹，此时保留状态数达到10⁴，使用的GPU显存小于12 GB.

A Study of the hydrodynamic behavior of cylindrical structure with double porous outer shelters

Porous structure can effectively reduce the loads caused by the water wave, which results in lowering the cost of engineering project. The double porous shelter performs even better. Therefore, it receives much attention from researches. However, most of the previous studies dealing with the analysis of the interaction between water wave are porous structure were based on two-dimensional plane wave assumption. This can hardly reflect the real phenomena of complex wave action. In this paper, a semi-analytical solution to the hydrodynamic interaction between the three-dimensional short-crested wave and the cylindrical structure with double porous shelters is performed by employing the scaled boundary finite element method (SBFEM). The SBFEM possesses the advantages of finite element method (FEM) and boundary element method (BEM): the spatial dimension of the problem is reduced by one, no fundamental solution is needed and no singularity occurs. Meanwhile, this method can meet the infinity of the boundary condition automatically. In the SBFEM, the total computational domain is divided into three sub-domains, two ring-shaped finite sub-domains and one outer infinite sub-domain. A variational principle approach is proposed to establish the SBFE governing equations, which describe the variation of the velocity potential of wave motion in the radial direction. Bessel functions and Hankel functions are chosen as the basis functions for the solution of bounded and unbounded sub-domain problems, respectively. Numerical examples show that the proposed approach achieves very high accuracy and converges rapidly with quite few discretized nodes at the outer boundary. In comparison with the cylindrical structure with single porous shelter, the former performs better for the reduction of the water wave force. In addition, The influences of the wave parameters and the configuration of the structure on the system hydrodynamics, including the wave force, wave and diffracted wave contour are extensively examined. This research provides a valuable insight into the hydrodynamic analysis of cylindrical structure with double porous shelters and their structural design.