基于GPU加速的深度重启Lanczos算法壳模型程序开发及应用

The nuclear properties in the ‘island of inversion’ and nuclear superdeformation around N,Z=20 are among the hot topics in the current nuclear physics studies. The multiple particle-hole excitations across sd-pf major shells play the fundamental role in these phenomena. The interacting shell model, in which the many-body wave functions are taken as the bases, is a powerful tool in the study of nuclear properties of the light-medium mass nuclei. However, with the increasing number and freedom of valence particles, the dimension of Hamiltonian matrix increases very rapidly, therefore the introduction of multiple particle-hole excitations poses a much higher demand for a shell model code. The open source NuShellX is the leading shell model code in the respect of speed, mainly due to the factorization of Hamiltonian matrix and application of thick-restart Lanczos algorithm. However the current NuShellX only can be run on the computers with shared memory. The maximum dimension which can be handled by NuShellX in a single node is still hard to meet the demand. General purpose GPU acceleration is particular suitable in the highly parallel computations with low cost. The extension of programming languages with GPU acceleration capabilities and the development of various arithmetic libraries greatly reduce the development cost of GPU parallelization. In this project we propose the development of a GPU accelerated thick-restart Lanczos code with open source linear algebra libraries, and the integrate with the NuShellX code. The new shell model code with GPU capabilities can handle the matrix with the dimension as large as O(109) in a GPU accelerated node. Then the effect of cross sd-pf major shell excitations on the N≈20 nuclei will be studied with the large-scale shell model. Through the proposed project, an open source shell model code with the GPU acceleration capabilities will be more versatile in the study of nuclear properties of the light-medium mass nuclei, and enables more close collaborations between the shell model physicists with the researches on the future large-scale nuclear physics scientific facilities in China.

反转岛核性质以及Z,N≈20近满壳核的超形变态是当前核物理研究的热点，跨sd-pf壳的多粒子空穴激发是这些现象出现的根源。相互作用壳模型是研究中轻质量原子核性质非常有力的工具，但随着价核子数目和自由度增加，壳模型哈密顿量矩阵维数急速增加。开源的壳模型程序NuShellX计算速度在众多壳模型程序中处于领先，但目前只能运行于内存共享的计算机上，大规模壳模型计算受到相当的限制。GPU是高性能并行计算的低成本解决方案。本项目拟以开源线性代数库为基础在国际上首次开发GPU加速的深度重启Lanczos算法程序，并结合NuShellX发展GPU加速的开源壳模型程序，使单节点GPU服务器能够处理J-表象下O(10^9)级别的矩阵，然后以大规模壳模型研究跨sd-pf壳激发对N≈20原子核性质影响。通过本项目的实施，新的开源壳模型程序能够更紧密地配合我国核物理大科学装置上的物理研究。

反转岛核性质以及Z,N≈20近满壳核的超形变态是当前核物理研究的热点，跨sd-pf壳 的多粒子空穴激发是这些现象出现的根源。相互作用壳模型是研究中轻质量原子核性质非常有力的工具，但随着价核子数目和自由度增加，壳模型哈密顿量矩阵维数急速增加，GPU是高性能并行计算的低成本解决方案。本项目基于开源的NuShellX和线性代数库为基础开发了GPU加速的壳模型程序，使单节点GPU服务器能够处理 J-表象下O(10^9)级别的矩阵，然后以大规模壳模型研究跨sd-pf壳激发对N≈20原子核性质影响。我们重点关注反转岛以及附近原子核的性质，提出通过计算静态四极矩以及跃迁四极矩推断原子核的四极形变参数的方法，并抽取了反转岛及附近原子核的形变信息。从壳模型计算结果来看，Mg同位素从22Mg至30Mg的三轴形变都比较小，我们预言了36Mg中可能存在较大的三轴形变。研究结果表明对于反转岛的电磁性质不仅取决于跨sd-pf大壳激发，而且与弱束缚轨道的有效电荷密切相关。