| 密度矩阵重正化群的异构并行优化 |
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| 引用本文： | 刘煜,刘伟庆. 密度矩阵重正化群的异构并行优化[J]. 物理学报, 2011, 60(12): 120202-120202. DOI: 10.7498/aps.60.120202 |
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| 作者姓名： | 刘煜 刘伟庆 |
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| 作者单位： | 1. 兰州大学物理科学与技术学院, 兰州 730000;2. 北京计算科学研究中心, 北京 100084 |
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| 基金项目： | 河南电力试验研究院科研基金资助的课题. |
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| 摘 要： | 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.
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| 关 键 词： | 密度矩阵重正化群 强关联格点模型 异构并行 |
| 收稿时间： | 2011-02-21 |
| 修稿时间： | 2011-07-05 |
A method of constructing peaked soliton solution of nonlinear wave equation by using smooth soliton solution |
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| Liu Yu and Liu Wei-Qing. A method of constructing peaked soliton solution of nonlinear wave equation by using smooth soliton solution[J]. Acta Physica Sinica, 2011, 60(12): 120202-120202. DOI: 10.7498/aps.60.120202 |
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| Authors: | Liu Yu and Liu Wei-Qing |
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| Affiliation: | 1. School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;2. Beijing Computational Science Research Center, Beijing 100084, China |
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| Abstract: | We propose a method of obtaining peakon solution from bell-shape smooth soliton (or solitary wave)solution, i.e. constructing directly an ansatz solution of peakon according to the well-known bell-shape smooth soliton solution and then determining the coefficients in ansatz solution. The method is verified to be feasible for four nonlinear wave equations and one set of equations. The bell-shape smooth soliton (or solitary wave)solution and peakon solution can exist in the same expression and the expressions of peakon solutions include those of the bell-shape smooth soliton solutions and the latter are the special cases of the former. |
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| Keywords: | nonlinear wave equation bell-shape smooth soliton(or solitary wave) solution peaked soliton (peakon)solution |
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