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Manuscript Title: OpenMP Fortran and C programs for solving the time-dependent Gross-Pitaevskii equation in an anisotropic trap
Authors: Luis E. Young-S., Dusan Vudragović, Paulsamy Muruganandam, Sadhan K. Adhikari, Antun Balaz
Program title: BEC-GP-OMP package, consisting of: (i) imag1d, (ii) imag2d, (iii) imag3d, (iv) imagaxi, (v) imagcir, (vi) imagsph, (vii) real1d, (viii) real2d, (ix) real3d, (x) realaxi, (xi) realcir, (xii) realsph.
Catalogue identifier: AEDU_v4_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 204(2016)209
Programming language: OpenMP C; OpenMP Fortran.
Computer: Any multi-core personal computer or workstation.
Operating system: Linux and Windows.
RAM: 1 GB.
Supplementary material: A pdf of the full manuscript for this version can be downloaded. It includes an individual summary for each of the above programs and the "Summary of revisions" information.
Keywords: Bose-Einstein condensate, Gross-Pitaevskii equation, Split-step Crank-Nicolson scheme, Real-and imaginary-time propagation, C program, Fortran program, OpenMP, Partial differential equation.
PACS: 02.60.Lj, 02.60.Jh, 02.60.Cb, 03.75.-b.
Classification: 2.9, 4.3, 4.12.

Does the new version supersede the previous version?: No. It does supersedes versions AEDU v1 0 and AEDU v2 0, but not AEDU v3 0, which is MPI-parallelized version.

Nature of problem:
The present OpenMP Fortran and C programs solve the time-dependent nonlinear partial differential Gross-Pitaevskii (GP) equation for a Bose-Einstein condensate in one (1D), two (2D), and three (3D) spatial dimensions in a harmonic trap with six different symmetries: axial- and radial-symmetry in 3D, circular-symmetry in 2D, and fully anisotropic in 2D and 3D.

Solution method:
The time-dependent GP equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation, in either imaginary or real time, over small time steps. The method yields the solution of stationary and/or non-stationary problems.

Reasons for new version:
Previously published Fortran and C programs [1,2] for solving the GP equation are recently enjoying frequent usage [3] and application to a more complex scenario of dipolar atoms [4]. They are also further extended to make use of general purpose graphics processing units (GPGPU) with Nvidia CUDA [5], as well as computer clusters using Message Passing Interface (MPI) [6]. However, a vast majority of users use single-computer programs, with which the solution of a realistic dynamical 1D problem, not to mention the more complicated 2D and 3D problems, could be time consuming. Now practically all computers have multicore processors, ranging from 2 up to 18 and more CPU cores. Some computers include motherboards with more than one physical CPU, further increasing the possible number of available CPU cores on a single computer to several tens. The present programs are parallelized using OpenMP over all the CPU cores and can significantly reduce the execution time. Furthermore, in the old version of the programs [1,2] the inputs were based on the mathematical quantity nonlinearity for the dimensionless form of the GP equation. The inputs for the present versions of programs are given in terms of phenomenological variables of experimental interest, as in Refs. [4,5], i.e., number of atoms, scattering length, harmonic oscillator length of the confining trap, etc. Also, the output files are given names which make identification of their contents easier, as in Refs. [4,5]. In addition, new output files for integrated densities of experimental interest are provided, and all programs were thoroughly revised to eliminate redundancies.

Summary of revisions:
See "Supplementary material" above.

Additional comments:
This package consists of 24 programs, see Program title above. For the particular purpose of each program, please see descriptions below.

Running time:
Example inputs provided with the programs take less than 30 minutes in a workstation with two Intel Xeon Processor E5-2650 v3, 2 QPI links, 10 CPU cores (25 MB cache, 2.3 GHz).

References:
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