The LISE package: Solvers for static and time-dependent superfluid local density approximation equations in three dimensions

Abstract

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the superfluid local density approximation (SLDA) and its extension to time-dependent situations, time-dependent superfluid local density approximation (TDSLDA), have been extensively used to describe various static and dynamical problems in nuclear physics, neutron star crust, and cold atom systems. In this paper, we present the codes that solve the static and time-dependent SLDA equations in three-dimensional coordinate space without any symmetry restriction. These codes are fully parallelized with the message passing interface (MPI) library and the time-dependent code takes advantage of graphic processing units (GPU) for accelerating execution. The dynamic code has checkpoint/restart capabilities and for initial conditions one can use any generalized Slater determinant type of wave function. By generating the appropriate initial quasi-particle wave-functions in a static calculation only, the time-dependent code can describe a large number of physical problems: nuclear fission, collisions of heavy ions, the interaction of quantized vortices with nuclei in the nuclear star crust, excitation of superfluid fermion systems by time dependent external fields, quantum shock waves, domain wall generation and propagation, the dynamics of the Anderson-Bogoliubov-Higgs mode, dynamics of fragmented condensates, vortex rings dynamics, generation and dynamics of quantized vortices, their crossing and recombinations and the incipient phases of quantum turbulence. Program summaryProgram title: LISECPC library link to program files:https://doi.org/10.17632/mwr7rsxpjw.1Licensing provisions: BSD 3-ClauseProgramming language: C, CUDANature of problem: The description of nuclear fission and nuclear reactions within the mean field approximation in real time within the extension of the density functional theory to superfluid systems is an extremely computationally demanding problem, which requires the solutions of a very large system of nonlinear coupled complex partial differential equations in 3+1 coordinates. Similar problems also appear in the case of cold atoms and in the dynamics of the neutron star crust, which have been tackled within the same framework with the same codes, using appropriate initial quasi-particle wave functions and/or an appropriate time-dependent external potential.Solution method: The evolution equations are discretized on a 3-dimensional spatial lattice and propagated in time. Spatial derivatives are evaluated using the fast Fourier transform technique. The propagation in time is performed using a predictor-modifier-corrector algorithm due to Adams-Bashforth-Milne, which requires only two evaluations of the right hand side of the equations per time step. The numerical accuracy of the time integration is ∼O(Δt)6. This method has a low truncation error, excellent numerical stability, and low roundoff errors.Additional comments including restrictions and unusual features: The code has been implemented on a variety of supercomputers (Jaguar, Titan, Piz Daint, Tsubame, Summit, Sierra) and demonstrates excellent scaling properties. The strong scaling capabilities can be significantly affected if a very large number of GPUs is used, when the communication time between processes overtakes the computation time as the dominant run time cost.