OpenMP Fortran programs for solving the time-dependent dipolar Gross-Pitaevskii equation

In this paper we present Open Multi-Processing (OpenMP) Fortran 90/95 versions of previously published numerical programs for solving the dipolar Gross-Pitaevskii (GP) equation including the contact interaction in one, two and three spatial dimensions. The atoms are considered to be polarized along the z axis and we consider different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar Bose-Einstein condensate (BEC) in one dimension (along x and z axes), two dimensions (in x -y and x -z planes), and three dimensions. The algorithm used is the split-step semi-implicit Crank-Nicolson scheme for imaginary-and real-time propagation to obtain stationary states and BEC dynamics, respectively, as in the previous version (Kishor Kumar et al., 2015 [3]). These OpenMP versions have significantly reduced execution time in multicore processors.New version program summaryProgram title: DBEC-GP-OMP, a program package containing programs imag3d-th.f90, real3d-th.f90, imag2dXY-th.f90, real2dXY-th.f90, imag2dXZ-th.f90, real2dXZ-th.f90, imag1dX-th.f90, real1dX-th.f90, imag1dZ-th.f90, real1dZ-th.f90, with fftw3.f03 and fftw3.mod. CPC Library link to program files: https://doi .org /10 .17632 /sp3wvbtnmh .1Licensing provisions: Apache License 2.0Programming language: Open Multi-Processing (OpenMP) Fortran 90/95. The program is tested with the GNU, Intel, and Oracle (former Sun) compilers. Journal reference of previous version: Comput. Phys. Commun. 195 (2015) 117. https://doi .org /10 .1016 /j .cpc . 2015 .03 .024Does the new version supersede the previous version?: Yes, Fortran programsNature of problem: The present OpenMP Fortran 90/95 programs solve the time-dependent nonlinear partial differential Gross-Pitaevskii (GP) equation for a trapped dipolar Bose-Einstein condensate (BEC) in one (1D), two (2D), and three (3D) spatial dimensions.Solution method: We employ the split-step Crank-Nicolson scheme to discretize the time-dependent GP equation in space and time. The discretized equation is then solved by imaginary-or real-time propagation, employing adequately small space and time steps, to yield the solution of stationary and non-stationary problems, respectively.Reason for new version: Previously published Fortran programs [1] for solving the GP equation for a BEC have become useful tools. These programs have been translated to the C programming language [2] and later extended to the more complex scenario of dipolar atoms [3], spinor condensates [4], and rotating condensates [5]. Now virtually all computers have multi-core processors and some have motherboards with more than one physical computer processing unit (CPU), which may increase the number of available CPU cores on a single computer to several tens. The Fortran [6] and C [7] programs for a nondipolar BEC have been adopted to be very fast on such multi-core modern computers. The C programs for a dipolar BEC have been adopted to multicore processors to yield OpenMP, OpenMP/MPI, and CUDA/MPI versions [8, 9].

Automated summary

In this paper, we present OpenMP Fortran 90/95 versions of numerical programs for solving the dipolar Gross-Pitaevskii equation. These programs have significantly reduced execution time on multicore processors.