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Manuscript Title: C programs for solving the time-dependent Gross-Pitaevskii equation in a
fully anisotropic trap | ||

Authors: Dusan Vudragović, Ivana Vidanović, Antun Balaz, Paulsamy Muruganandam, Sadhan K. Adhikari | ||

Program title: GP-SCL package, consisting of: (i) imagtime1d, (ii) imagtime2d, (iii) imagtime2d-th, (iv) imagtimecir, (v) imagtime3d, (vi) imagtime3d-th, (vii) imagtimeaxial, (viii) imagtimeaxial-th, (ix) imagtimesph, (x) realtime1d, (xi) realtime2d, (xii) realtime2d-th, (xiii) realtimecir, (xiv) realtime3d, (xv) realtime3d-th, (xvi) realtimeaxial, (xvii) realtimeaxial-th, (xviii) realtimesph | ||

Catalogue identifier: AEDU_v2_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 183(2012)2021 | ||

Programming language: C and C/OpenMP. | ||

Computer: Any modern computer with C language compiler installed. | ||

Operating system: Linux, Unix, Mac OS, Windows. | ||

Has the code been vectorised or parallelized?: Yes. Parallelized with OpenMp. | ||

RAM: Memory used with the supplied input files: 2-4 MByte (i, iv, ix, x, xiii, xvi, xvii, xviii), 8 MByte (xi, xii), 32 MByte (vii, viii), 80 MByte (ii, iii), 700 MByte (xiv, xv), 1.2 GByte (v, vi) | ||

Keywords: Bose-Einstein condensate, Gross-Pitaevskii equation, Split-step Crank-Nicolson scheme, Real- and imaginary-time propagation, C 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 | ||

Nature of problem:These programs are designed to solve the time-dependent Gross-Pitaevskii (GP) nonlinear partial differential equation in one-, two- or three-space dimensions with a harmonic, circularly-symmetric, spherically- symmetric, axially-symmetric or fully anisotropic trap. The GP equation describes the properties of a dilute trapped Bose-Einstein condensate. | ||

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:Previous Fortran programs [1] are used within the ultra-cold atoms [2-11] and nonlinear optics [12,13] communities, as well as in various other fields [14-16]. This new version represents translation of all programs to the C programing language, which will make it accessible to the wider parts of the corresponding communities. It is well known that numerical simulations of the GP equation in highly experimentally relevant geometries with two or three space variables are computationally very demanding, which presents an obstacle in detailed numerical studies of such systems. For this reason, we have developed threaded (OpenMP parallelized) versions of programs imagtime2d, imagtime3d, imagtimeaxial, realtime2d, realtime3d, realtimeaxial, which are named imagtime2d-th, imagtime3d-th, imagtimeaxial-th, realtime2d-th, realtime3d-th, realtimeaxial-th, respectively. Figures showing the scalability results obtained for the OpenMp versions of the programs realtime2d and realtime3d are given in the paper, a copy of which is included in the distribution file. These figures show that the speedup is almost linear, and on a computer with the total of 8 CPU cores we observe a maximal speedup of around 7, or roughly 90% of the ideal speedup, while on a computer with 12 CPU cores we find that the maximal speedup is around 9.6, or 80% of the ideal speedup. Such a speedup represents significant improvement in the performance. | ||

Summary of revisions:All Fortran programs from the previous version [1] are translated to C and named in the same way. The structure of all programs is identical. We have introduced the use of comprehensive input files, where all parameters are explained in detail and can be set by a user. We have also included makefiles with tested and verified settings for GNU's gcc compiler, Intel's icc compiler, IBM's xlc compiler, PGI's pgcc compiler, and Sun's suncc (former Oracle's) compiler. In addition to this, 6 new threaded (OpenMP parallelized) programs are supplied (imagtime2d-th, imagtime3d-th, imagtimeaxial-th, realtime2d-th, realtime3d-th, realtimeaxial-th) for algorithms involving two or three space variables. They are written by OpenMP-parallelizing the most computationally demanding loops in functions performing time evolution (calcnu, calclux, calcluy, calcluz), normalization (calcnorm), and calculation of physical quantities (calcmuen, calcrms). Since some of the dynamically allocated array variables are used within such loops, they had to be made private for each thread. This was done by allocating matrices instead of arrays, with the first index in all such matrices corresponding to a thread number. | ||

Additional comments:This package consists of 18 programs, see Program title above, out of which 12 programs (i, ii, iv, v, vii, ix, x, xi, xiii, xiv, xvi, xviii) are serial, while 6 programs (iii, vi, viii, xii, xv, xvii) are threaded (OpenMP parallelized). For the particular purpose of each program, please see descriptions in the pdf file included in the distribution file. | ||

Running time:All running times given in descriptions below refer to programs compiled with gcc on quad-core Intel Xeon X5460 at 3.16 GHz (CPU1), and programs compiled with icc on quad-core Intel Nehalem E5540 at 2.53 GHz (CPU2). With the supplied input files, running times on CPU1 are: 5 minutes (i, iv, ix, xii, xiii, xvii, xviii), 10 minutes (viii, xvi), 15 minutes (iii, x, xi), 30 minutes (ii, vi, vii), 2 hours (v), 4 hours (xv), 15 hours (xiv). On CPU2, running times are: 5 minutes (i, iii, iv, viii, ix, xii, xiii, xvi, xvii, xviii), 10 minutes (vi, x, xi), 20 minutes (ii, vii), 1 hour (v), 2 hours (xv), 12 hours (xiv). | ||

References: | ||

[1] | P. Muruganandam, S. K. Adhikari, Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap, Comput. Phys. Commun. 180 (2009) 1888. | |

[2] | G. Mazzarella, L. Salasnich, Collapse of triaxial bright solitons in atomic Bose-Einstein condensates, Phys. Lett. A 373 (2009) 4434. | |

[3] | Y. Cheng, S. K. Adhikari, Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice, Phys. Rev. A 81 (2010) 023620; S. K. Adhikari, H. Lu, H. Pu, Self-trapping of a Fermi superfluid in a double-well potential in the Bose-Einstein-condensate-unitarity crossover, Phys. Rev. A 80 (2009) 063607. | |

[4] | S. Gautam, D. Angom, Rayleigh-Taylor instability in binary condensates, Phys. Rev. A 81 (2010) 053616; S. Gautam, D. Angom, Ground state geometry of binary condensates in axisymmetric traps, J. Phys. B 43 (2010) 095302; S. Gautam, P. Muruganandam, D. Angom, Position swapping and pinching in Bose-Fermi mixtures with two-color optical Feshbach resonances, Phys. Rev. A 83 (2011) 023605. | |

[5] | S. K. Adhikari, B. A. Malomed, L. Salasnich, F. Toigo, Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials, Phys. Rev. A 81 (2010) 053630. | |

[6] | G. K. Chaudhary, R. Ramakumar, Collapse dynamics of a (176)Yb-(174)Yb Bose-Einstein condensate, Phys. Rev. A 81 (2010) 063603. | |

[7] | S. Sabari, R. V. J. Raja, K. Porsezian, P. Muruganandam, Stability of trapless Bose-Einstein condensates with two- and three-body interactions, J. Phys. B 43 (2010) 125302. | |

[8] | L. E. Young-S, L. Salasnich, S. K. Adhikari, Dimensional reduction of a binary Bose-Einstein condensate in mixed dimensions, Phys. Rev. A 82 (2010) 053601. | |

[9] | I. Vidanović, A. Balaz, H. Al-Jibbouri, A. Pelster, Nonlinear Bose-Einstein-condensate dynamics induced by a harmonic modulation of the s-wave scattering length, Phys. Rev. A 84 (2011) 013618. | |

[10] | R. R. Sakhel, A. R. Sakhel, H. B. Ghassib, Self-interfering matter-wave patterns generated by a moving laser obstacle in a two-dimensional Bose-Einstein condensate inside a power trap cut off by box potential boundaries, Phys. Rev. A 84 (2011) 033634. | |

[11] | A. Balaz, A. I. Nicolin, Faraday waves in binary nonmiscible Bose-Einstein condensates, Phys. Rev. A 85 (2012) 023613; A. I. Nicolin, Variational treatment of Faraday waves in inhomogeneous Bose-Einstein condensates, Physica A 391 (2012) 1062; A. I. Nicolin, Resonant wave formation in Bose-Einstein condensates, Phys. Rev. E 84 (2011) 056202; A. I. Nicolin, Faraday waves in Bose-Einstein condensates subject to anisotropic transverse confinement, Rom. Rep. Phys. 63 (2011) 1329; A. I. Nicolin, M. C. Raportaru, Faraday waves in high-density cigar-shaped BoseEinstein condensates, Physica A 389 (2010) 4663. | |

[12] | S. Yang, M. Al-Amri, J. Evers, M. S. Zubairy, Controllable optical switch using a Bose-Einstein condensate in an optical cavity, Phys. Rev. A 83 (2011) 053821. | |

[13] | W. Hua, X.-S. Liu, Dynamics of cubic and quintic nonlinear Schrodinger equations, Acta Phys. Sin. 60 (2011) 110210. | |

[14] | Z. Sun, W. Yang, An exact short-time solver for the time-dependent Schrodinger equation, J. Chem. Phys. 134 (2011) 041101. | |

[15] | A. Balaz, I. Vidanović, A. Bogojević, A. Belić, A. Pelster, Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator, J. Stat. Mech.-Theory Exp. (2011) P03004. | |

[16] | W. B. Cardoso, A. T. Avelar, D. Bazeia, One-dimensional reduction of the three-dimenstional Gross-Pitaevskii equation with two- and three-body interactions, Phys. Rev. E 83 (2011) 036604. |

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