Thick-restart block Lanczos method for large-scale shell-model calculations

Abstract

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. Program summaryProgram Title: KSHELLProgram Files doi:http://dx.doi.org/10.17632/kgzdz6ryyk.1Licensing provisions: GPLv3Programming language: Fortran 90Nature of problem: The nuclear shell-model calculation is one of the configuration interaction methods in nuclear physics to study nuclear structure. The model space is spanned by the M-scheme basis states. We obtain nuclear wave functions by solving an eigenvalue problem of the shell-model Hamiltonian matrix, which is a sparse, symmetric matrix.Solution method: The KSHELL code enables us to solve the eigenvalue problem of the shell-model Hamiltonian matrix utilizing the thick-restart Lanczos or thick-restart block Lanczos methods. Since the number of the matrix elements are too huge to be stored, the elements are generated on the fly at every matrix–vector product. The overhead of the on-the-fly algorithm are reduced by the block Lanczos method.Additional comments including restrictions and unusual features: The KSHELL code is equipped with a user-friendly dialog interface to generate a shell script to run a job. The program runs both on a single node and a massively parallel computer. It provides us with energy levels, spin, isospin, magnetic and quadrupole moments, E2/M1 transition probabilities and one-particle spectroscopic factors. Up to tens of billions M-scheme dimension is capable, if enough memory is available.