厚重启动块Lanczos法在大型壳模型计算中的应用
Thick-Restart Block Lanczos Method for Large-Scale Shell-Model Calculations
摘要：
我们提出了一个厚重启动块Lanczos方法，这是一个扩展的厚重启动Lanczos方法与块算法，作为一个大规模的壳模型计算的特征值求解器。与传统的Lanczos方法相比，该方法具有两个优点：一是可以精确计算近简并特征值，二是可以有效地计算大量特征值。这些特征对于计算本征值密度相当高的高激发态是相当有利的。壳模型代码，命名为KSHELL，配备了这种方法开发的大规模并行计算，它使我们能够揭示核统计特性，最近的实验设施进行了深入研究。我们描述的算法和性能的KSHELL码，并证明，本方法优于传统的Lanczos方法。
英文摘要：
We propose a thick-restart block Lanczos method, which is an extension of the thick-restart Lanczos method with the block algorithm, as an eigensolver of the large-scale shell-model calculations. This method has two advantages over the conventional Lanczos method: the precise computations of the near-degenerate eigenvalues, and the efficient computations for obtaining a large number of eigenvalues. These features are quite advantageous to compute highly excited states where the eigenvalue density is rather high. A shell-model code, named KSHELL, equipped with this method was developed for massively parallel computations, and it enables us to reveal nuclear statistical properties which are intensively investigated by recent experimental facilities. We describe the algorithm and performance of the KSHELL code and demonstrate that the present method outperforms the conventional Lanczos method.
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