Programs in Physics & Physical Chemistry
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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_0|
Distribution 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.
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  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  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.
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.
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).
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