We present OpenMP versions of FORTRAN programs for solving the Gross–Pitaevskii equation for a harmonically trapped three-component spin-1 spinor Bose–Einstein condensate (BEC) in one (1D) and two ...(2D) spatial dimensions with or without spin–orbit (SO) and Rabi couplings. Several different forms of SO coupling are included in the programs. We use the split-step Crank–Nicolson discretization for imaginary- and real-time propagation to calculate stationary states and BEC dynamics, respectively. The imaginary-time propagation programs calculate the lowest-energy stationary state. The real-time propagation programs can be used to study the dynamics. The simulation input parameters are provided at the beginning of each program. The programs propagate the condensate wave function and calculate several relevant physical quantities. Outputs of the programs include the wave function, energy, root-mean-square sizes, different density profiles (linear density for the 1D program, linear and surface densities for the 2D program). The imaginary- or real-time propagation can start with an analytic wave function or a pre-calculated numerical wave function. The imaginary-time propagation usually starts with an analytic wave function, while the real-time propagation is often initiated with the previously calculated converged imaginary-time wave function.
Program title: BEC-GP-SPINOR, consisting of: BEC-GP-SPINOR-OMP package, containing programs spin-SO-imre1d-omp.f90 and spin-SO-imre2d-omp.f90, with util.f90.
CPC Library link to program files:https://doi.org/10.17632/j3wr4wn946.1
Licensing provisions: Apache License 2.0
Programming language: OpenMP FORTRAN. The FORTRAN programs are tested with the GNU, Intel, PGI, and Oracle compiler.
Nature of problem: The present Open Multi-Processing (OpenMP) FORTRAN programs solve the time-dependent nonlinear partial differential Gross–Pitaevskii (GP) equation for a trapped spinor Bose–Einstein condensate, with or without spin–orbit coupling, in one and two spatial dimensions.
Solution method: We employ the split-step Crank–Nicolson rule 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.
Many of the static and dynamic properties of an atomic Bose–Einstein condensate (BEC) are usually studied by solving the mean-field Gross–Pitaevskii (GP) equation, which is a nonlinear partial ...differential equation for short-range atomic interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank–Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x–y and x–z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas–Fermi approximations.
Program title: (i) imag1dZ, (ii) imag1dX, (iii) imag2dXY, (iv) imag2dXZ, (v) imag3d, (vi) real1dZ, (vii) real1dX, (viii) real2dXY, (ix) real2dXZ, (x) real3d
Catalogue identifier: AEWL_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWL_v1_0.html
Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 111384
No. of bytes in distributed program, including test data, etc.: 604013
Distribution format: tar.gz
We present C programming language versions of earlier published Fortran programs (Muruganandam and Adhikari (2009) 1) for calculating both stationary and non-stationary solutions of the ...time-dependent Gross–Pitaevskii (GP) equation. The GP equation describes the properties of dilute Bose–Einstein condensates at ultra-cold temperatures. C versions of programs use the same algorithms as the Fortran ones, involving real- and imaginary-time propagation based on a split-step Crank–Nicolson method. In a one-space-variable form of the GP equation, we consider the one-dimensional, two-dimensional, circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form, we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. In addition to these twelve programs, for six algorithms that involve two and three space variables, we have also developed threaded (OpenMP parallelized) programs, which allow numerical simulations to use all available CPU cores on a computer. All 18 programs are optimized and accompanied by makefiles for several popular C compilers. We present typical results for scalability of threaded codes and demonstrate almost linear speedup obtained with the new programs, allowing a decrease in execution times by an order of magnitude on modern multi-core computers.
New version program summary
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.
Program Summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDU_v2_0.html.
Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland.
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html.
No. of lines in distributed program, including test data, etc.: 180583.
No. of bytes in distributed program, including test data, etc.: 1188688.
Distribution format: tar.gz.
Programming language: C and C/OpenMP.
Computer: Any modern computer with C language compiler installed.
Operating system: Linux, Unix, Mac OS, Windows.
RAM: Memory used with the supplied input files: 2–4 MB (i, iv, ix, x, xiii, xvi, xvii, xviii), 8 MB (xi, xii), 32 MB (vii, viii), 80 MB (ii, iii), 700 MB (xiv, xv), 1.2 GB (v, vi).
Number of processors used: For threaded (OpenMP parallelized) programs, all available CPU cores on the computer.
Classification: 2.9, 4.3, 4.12.
Catalogue identifier of previous version: AEDU_v1_0.
Journal reference of previous version: Comput. Phys. Commun. 180 (2009) 1888.
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 solutions of stationary and/or non-stationary problems.
Reasons for the 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 programming 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. Fig. 1 shows the scalability results obtained for OpenMP versions of programs realtime2d and realtime3d. As we can see, the speedup is almost linear, and on a computer with the total of 8 CPU cores we observe in Fig. 1(a) a maximal speedup of around 7, or roughly 90% of the ideal speedup, while on a computer with 12 CPU cores we find in Fig. 1(b) 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 Oracle’s suncc (former Sun’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 below.
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 min (i, iv, ix, xii, xiii, xvii, xviii), 10 min (viii, xvi), 15 min (iii, x, xi), 30 min (ii, vi, vii), 2 h (v), 4 h (xv), 15 h (xiv). On CPU2, running times are: 5 min (i, iii, iv, viii, ix, xii, xiii, xvi, xvii, xviii), 10 min (vi, x, xi), 20 min (ii, vii), 1 h (v), 2 h (xv), 12 h (xiv).
We present Open Multi-Processing (OpenMP) version of Fortran 90 programs for solving the Gross–Pitaevskii (GP) equation for a Bose–Einstein condensate in one, two, and three spatial dimensions, ...optimized for use with GNU and Intel compilers. We use the split-step Crank–Nicolson algorithm for imaginary- and real-time propagation, which enables efficient calculation of stationary and non-stationary solutions, respectively. The present OpenMP programs are designed for computers with multi-core processors and optimized for compiling with both commercially-licensed Intel Fortran and popular free open-source GNU Fortran compiler. The programs are easy to use and are elaborated with helpful comments for the users. All input parameters are listed at the beginning of each program. Different output files provide physical quantities such as energy, chemical potential, root-mean-square sizes, densities, etc. We also present speedup test results for new versions of the programs.
Program title: BEC-GP-OMP-FOR software package, consisting of: (i) imag1d-th, (ii) imag2d-th, (iii) imag3d-th, (iv) imagaxi-th, (v) imagcir-th, (vi) imagsph-th, (vii) real1d-th, (viii) real2d-th, (ix) real3d-th, (x) realaxi-th, (xi) realcir-th, (xii) realsph-th.
Program files doi:http://dx.doi.org/10.17632/y8zk3jgn84.2
Licensing provisions: Apache License 2.0
Programming language: OpenMP GNU and Intel Fortran 90.
Computer: Any multi-core personal computer or workstation with the appropriate OpenMP-capable Fortran compiler installed.
Number of processors used: All available CPU cores on the executing computer.
Journal reference of previous version: Comput. Phys. Commun. 180 (2009) 1888; ibid.204 (2016) 209.
Does the new version supersede the previous version?: Not completely. It does supersede previous Fortran programs from both references above, but not OpenMP C programs from Comput. Phys. Commun. 204 (2016) 209.
Nature of problem: The present Open Multi-Processing (OpenMP) Fortran programs, optimized for use with commercially-licensed Intel Fortran and free open-source GNU Fortran compilers, solve the time-dependent nonlinear partial differential (GP) equation for a trapped Bose–Einstein condensate in one (1d), two (2d), and three (3d) spatial dimensions for six different trap symmetries: axially and radially symmetric traps in 3d, circularly symmetric traps in 2d, fully isotropic (spherically symmetric) and fully anisotropic traps in 2d and 3d, as well as 1d traps, where no spatial symmetry is considered.
Solution method: We employ the split-step Crank–Nicolson algorithm 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.
Reasons for the new version: Previously published Fortran programs 1,2 have now become popular tools 3 for solving the GP equation. These programs have been translated to the C programming language 4 and later extended to the more complex scenario of dipolar atoms 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 C programs have been adopted to be very fast on such multi-core modern computers using general-purpose graphic processing units (GPGPU) with Nvidia CUDA and computer clusters using Message Passing Interface (MPI) 6. Nevertheless, previously developed Fortran programs are also commonly used for scientific computation and most of them use a single CPU core at a time in modern multi-core laptops, desktops, and workstations. Unless the Fortran programs are made aware and capable of making efficient use of the available CPU cores, the solution of even a realistic dynamical 1d problem, not to mention the more complicated 2d and 3d problems, could be time consuming using the Fortran programs. Previously, we published auto-parallel Fortran programs 2 suitable for Intel (but not GNU) compiler for solving the GP equation. Hence, a need for the full OpenMP version of the Fortran programs to reduce the execution time cannot be overemphasized. To address this issue, we provide here such OpenMP Fortran programs, optimized for both Intel and GNU Fortran compilers and capable of using all available CPU cores, which can significantly reduce the execution time.
Summary of revisions: Previous Fortran programs 1 for solving the time-dependent GP equation in 1d, 2d, and 3d with different trap symmetries have been parallelized using the OpenMP interface to reduce the execution time on multi-core processors. There are six different trap symmetries considered, resulting in six programs for imaginary-time propagation and six for real-time propagation, totaling to 12 programs included in BEC-GP-OMP-FOR software package.
All input data (number of atoms, scattering length, harmonic oscillator trap length, trap anisotropy, etc.) are conveniently placed at the beginning of each program, as before 2. Present programs introduce a new input parameter, which is designated by Number_of_Threads and defines the number of CPU cores of the processor to be used in the calculation. If one sets the value 0 for this parameter, all available CPU cores will be used. For the most efficient calculation it is advisable to leave one CPU core unused for the background system’s jobs. For example, on a machine with 20 CPU cores such that we used for testing, it is advisable to use up to 19 CPU cores. However, the total number of used CPU cores can be divided into more than one job. For instance, one can run three simulations simultaneously using 10, 4, and 5 CPU cores, respectively, thus totaling to 19 used CPU cores on a 20-core computer.
The Fortran source programs are located in the directory src, and can be compiled by the make command using the makefile in the root directory BEC-GP-OMP-FOR of the software package. The examples of produced output files can be found in the directory output, although some large density files are omitted, to save space. The programs calculate the values of actually used dimensionless nonlinearities from the physical input parameters, where the input parameters correspond to the identical nonlinearity values as in the previously published programs 1, so that the output files of the old and new programs can be directly compared. The output files are conveniently named such that their contents can be easily identified, following the naming convention introduced in Ref. 2. For example, a file named -out.txt, where is a name of the individual program, represents the general output file containing input data, time and space steps, nonlinearity, energy and chemical potential, and was named fort.7 in the old Fortran version of programs 1. A file named -den.txt is the output file with the condensate density, which had the names fort.3 and fort.4 in the old Fortran version 1 for imaginary- and real-time propagation programs, respectively. Other possible density outputs, such as the initial density, are commented out in the programs to have a simpler set of output files, but users can uncomment and re-enable them, if needed. In addition, there are output files for reduced (integrated) 1d and 2d densities for different programs. In the real-time programs there is also an output file reporting the dynamics of evolution of root-mean-square sizes after a perturbation is introduced. The supplied real-time programs solve the stationary GP equation, and then calculate the dynamics. As the imaginary-time programs are more accurate than the real-time programs for the solution of a stationary problem, one can first solve the stationary problem using the imaginary-time programs, adapt the real-time programs to read the pre-calculated wave function and then study the dynamics. In that case the parameter NSTP in the real-time programs should be set to zero and the space mesh and nonlinearity parameters should be identical in both programs. The reader is advised to consult our previous publication where a complete description of the output files is given 2. A readme.txt file, included in the root directory, explains the procedure to compile and run the programs.
We tested our programs on a workstation with two 10-core Intel Xeon E5-2650 v3 CPUs. The parameters used for testing are given in sample input files, provided in the corresponding directory together with the programs. In Table 1 we present wall-clock execution times for runs on 1, 6, and 19 CPU cores for programs compiled using Intel and GNU Fortran compilers. The corresponding columns “Intel speedup” and “GNU speedup” give the ratio of wall-clock execution times of runs on 1 and 19 CPU cores, and denote the actual measured speedup for 19 CPU cores. In all cases and for all numbers of CPU cores, although the GNU Fortran compiler gives excellent results, the Intel Fortran compiler turns out to be slightly faster. Note that during these tests we always ran only a single simulation on a workstation at a time, to avoid any possible interference issues. Therefore, the obtained wall-clock times are more reliable than the ones that could be measured with two or more jobs running simultaneously. We also studied the speedup of the programs as a function of the number of CPU cores used. The performance of the Intel and GNU Fortran compilers is illustrated in Fig. 1, where we plot the speedup and actual wall-clock times as functions of the number of CPU cores for 2d and 3d programs. We see that the speedup increases monotonically with the number of CPU cores in all cases and has large values (between 10 and 14 for 3d programs) for the maximal number of cores. This fully justifies the development of OpenMP programs, which enable much faster and more efficient solving of the GP equation.
Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the ...interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.
The social media revolution is having a dramatic effect on the world of scientific publication. Scientists now publish their research interests, theories and outcomes across numerous channels, ...including personal blogs and other thematic web spaces where ideas, activities and partial results are discussed. Accordingly, information systems that facilitate access to scientific literature must learn to cope with this valuable and varied data, evolving to make this research easily discoverable and available to end users. In this paper we describe the incremental process of discovering web resources in the domain of agricultural science and technology. Making use of Linked Open Data methodologies, we interlink a wide array of custom-crawled resources with the AGRIS bibliographic database in order to enrich the user experience of the AGRIS website. We also discuss the SemaGrow Stack, a query federation and data integration infrastructure used to estimate the semantic distance between crawled web resources and AGRIS.
Over the period of six years and three phases, the SEE-GRID programme has established a strong regional human network in the area of distributed scientific computing and has set up a powerful ...regional Grid infrastructure. It attracted a number of user communities and applications from diverse fields from countries throughout the South-Eastern Europe. From the infrastructure point view, the first project phase has established a pilot Grid infrastructure with more than 20 resource centers in 11 countries. During the subsequent two phases of the project, the infrastructure has grown to currently 55 resource centers with more than 6,600 CPUs and 750 TBs of disk storage, distributed in 16 participating countries. Inclusion of new resource centers to the existing infrastructure, as well as a support to new user communities, has demanded setup of regionally distributed core services, development of new monitoring and operational tools, and close collaboration of all partner institution in managing such a complex infrastructure. In this paper we give an overview of the development and current status of SEE-GRID regional infrastructure and describe its transition to the NGI-based Grid model in EGI, with the strong SEE regional collaboration.
VI-SEEM DREAMCLIMATE Service Vudragovic, Dusan; Ilic, Luka; Jovanovic, Petar ...
Scalable Computing. Practice and Experience,
06/2018, Letnik:
19, Številka:
2
Journal Article
Recenzirano
Premature human mortality due to cardiopulmonary disease and lung cancer is found in epidemiological studies to be correlated to increased levels of atmospheric particulate matter. Such negative dust ...effects on the human mortality in the North Africa - Europe - Middle East region can be successfully studied by the DREAM dust model. However, to assess health effects of dust and its other impacts on the environment, a detailed modelling of the climate for a period of one year in a high-resolution mode is required. We describe here a parallel implementation of the DREAM dust model, the DREAMCLIMATE service, which is optimised for use on the high-performance regional infrastructure provided by the VI-SEEM project. In addition to development and integration of this service, we also present a use-case study of premature mortality due to desert dust in the North Africa - Europe - Middle East region for the year 2005, to demonstrate how the newly deployed service can be used.
We present new version of previously published Fortran and C programs for solving the Gross–Pitaevskii equation for a Bose–Einstein condensate with contact interaction in one, two and three spatial ...dimensions in imaginary and real time, yielding both stationary and non-stationary solutions. To reduce the execution time on multicore processors, new versions of parallelized programs are developed using Open Multi-Processing (OpenMP) interface. The input in the previous versions of programs was the mathematical quantity nonlinearity for dimensionless form of Gross–Pitaevskii equation, whereas in the present programs the inputs are quantities of experimental interest, such as, number of atoms, scattering length, oscillator length for the trap, etc. New output files for some integrated one- and two-dimensional densities of experimental interest are given. We also present speedup test results for the new programs.
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.
Program Summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v4_0.html
Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland.
Licensing provisions: Apache License 2.0
No. of lines in distributed program, including test data, etc.: 130308.
No. of bytes in distributed program, including test data, etc.: 929062.
Distribution format: tar.gz.
Programming language: OpenMP C; OpenMP Fortran.
Computer: Any multi-core personal computer or workstation.
Operating system: Linux and Windows.
RAM: 1 GB.
Number of processors used: All available CPU cores on the executing computer.
Classification: 2.9, 4.3, 4.12.
Catalogue identifier of previous version: AEDU_v1_0, AEDU_v2_0.
Journal reference of previous version: Comput. Phys. Commun. 180 (2009) 1888; ibid. 183 (2012) 2021.
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 the 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: Previous Fortran 1 and C 2 programs for the solution of time-dependent GP equation in 1D, 2D, and 3D with different trap symmetries have been modified to achieve two goals. First, they are parallelized using OpenMP interface to reduce the execution time in multicore processors. Previous C programs 2 had OpenMP-parallelized versions of 2D and 3D programs, together with the serial versions, while here all programs are OpenMP-parallelized. Secondly, the programs now have input and output files with quantities of phenomenological interest. There are six trap symmetries and both in C and in Fortran there are twelve programs, six for imaginary-time propagation and six for real-time propagation, totaling to 24 programs. In 3D, we consider full radial symmetry, axial symmetry and full anisotropy. In 2D, we consider circular symmetry and full anisotropy. The structure of all programs is similar.
For the Fortran programs the input data (number of atoms, scattering length, harmonic oscillator trap length, trap anisotropy, etc.) are conveniently placed at the beginning of each program. For the C programs the input data are placed in separate input files, examples of which can be found in a directory named input. The examples of output files for both Fortran and C programs are placed in the corresponding directories called output. The programs then calculate the dimensionless nonlinearities actually used in the calculation. The provided programs use physical input parameters that give identical nonlinearity values as the previously published programs 1,2, so that the output files of the old and new programs can be directly compared. The output files are conveniently named so that their contents can be easily identified, following Refs. 4,5. For example, file named -out.txt, where is a name of the individual program, is the general output file containing input data, time and space steps, nonlinearity, energy and chemical potential, and was named fort.7 in the old Fortran version. The file -den.txt is the output file with the condensate density, which had the names fort.3 and fort.4 in the old Fortran version for imaginary- and real-time propagation, respectively. Other density outputs, such as the initial density, are commented out to have a simpler set of output files. The users can re-introduce those by taking out the comment symbols, if needed. Table 1Wall-clock execution times (in seconds) for runs with 1, 6 and 20 CPU cores with different programs using the Intel Fortran ifort (F-1, F-6 and F-20, respectively) and Intel C icc (C-1, C-6 and C-20, respectively) compilers using a workstation with two Intel Xeon E5-2650 v3 CPUs, with a total of 20 CPU cores, and obtained speedups (speedup-F=F-1/F-20, -speedupC=C-1/C-20 ) for 20 CPU cores.F-1F-6F-20speedup-FC-1C-6C-20speedup-Cimag1d3226261.24528271.7imagcir1515151.02115151.4imagsph1212121.01912101.9real1d19484722.7304110983.1realcir13262572.318278642.8realsph11968671.819176613.1imag2d19066523.7394773311.9imagaxi24074564.3499113559.1real2d26970475.7483963513.8realaxi13237255.3237512210.8imag3d16824723664.6249054520212.3real3d15,479349420827.422,2284558143815.5 Display omitted
Also, some new output files are introduced in this version of programs. The files -rms.txt are the output files with values of root-mean-square (rms) sizes in the multi-variable cases. There are new files with integrated densities, such as imag2d-den1d_x.txt, where the first part (imag2d) denotes that the density was calculated with the 2D program imag2d, and the second part (den1d_x) stands for the 1D density in the x-direction, obtained after integrating out the 2D density |ϕ(x,y)|2 in the x–y plane over y-coordinate,(1)n1D(x)=∫−∞∞dy|ϕ(x,y)|2. Similarly, imag3d-den1d_x.txt and real3d-den1d_x.txt represent 1D densities from a 3D calculation obtained after integrating out the 3D density |ϕ(x,y,z)|2 over y- and z-coordinate. The files imag3d-den2d_xy.txt and real3d-den2d_xy.txt are the integrated 2D densities in the x–y plane from a 3D calculation obtained after integrating out the 3D density over the z-coordinate, and similarly for other output files. Again, calculation and saving of these integrated densities is commented out in the programs, and can be activated by the user, if needed.
In real-time propagation programs there are additional results for the dynamics saved in files, such as real2d-dyna.txt, where the first column denotes time, the second, third and fourth columns display rms sizes for the x-, y-, and r-coordinate, respectively. The dynamics is generated by multiplying the nonlinearity with a pre-defined factor during the NRUN iterations, and starting with the wave function calculated during the NPAS iterations. Such files were named fort.8 in the old Fortran versions of programs. There are similar files in the 3D real-time programs as well.
Often it is needed to get a precise stationary state solution by imaginary-time propagation and then use it in the study of dynamics using real-time propagation. For that purpose, if the integer number NSTP is set to zero in real-time propagation, the density obtained in the imaginary-time simulation is used as initial wave function for real-time propagation, as in Refs. 4,5. In addition, at the end of output files -out.txt, we have introduced two new outputs, wall-clock execution time and CPU time for each run.
We tested our programs on a workstation with two 10-core Int
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