Hybrid OpenMP/MPI programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

We present hybrid OpenMP/MPI (Open Multi-Processing/Message Passing Interface) parallelized versions of earlier published C programs (D. Vudragovi\'{c} et al. (2012) [1]) for calculating both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation in three spatial dimensions. The GP equation describes the properties of dilute Bose-Einstein condensates at ultra-cold temperatures. Hybrid versions of programs use the same algorithms as the C ones, involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method, but consider only a fully-anisotropic three-dimensional GP equation, where algorithmic complexity for large grid sizes necessitates parallelization in order to reduce execution time and/or memory requirements per node. Since distributed memory approach is required to address the latter, we combine MPI programing paradigm with existing OpenMP codes, thus creating fully flexible parallelism within a combined distributed/shared memory model, suitable for different modern computer architectures. The two presented C/OpenMP/MPI programs for real- and imaginary-time propagation are optimized and accompanied by a customizable makefile. We present typical scalability results for the provided OpenMP/MPI codes and demonstrate almost linear speedup until inter-process communication time starts to dominate over calculation time per iteration. Such a scalability study is necessary for large grid sizes in order to determine optimal number of MPI nodes and OpenMP threads per node.

Previous versions of this program (AEDU_v1_0 and AEDU_v2_0) may be found at dx.doi.org/10.1016/j.cpc.2009.04.015 and dx.doi.org/10.1016/j.cpc.2012.03.022 respectively. The original version of this dataset (http://dx.doi.org/10.17632/hrk84bznv2.1) contains a typo in one source file, which has been corrected in the present version.

本报告呈现了先前已发表的 C 程序（D. Vudragović 等，2012 [1]）的混合 OpenMP/MPI（开放多处理/消息传递接口）并行化版本，用于计算三维空间中时间依赖的 Gross-Pitaevskii（GP）方程的稳态和非稳态解。GP 方程描述了在超低温下稀薄玻色-爱因斯坦凝聚体的性质。混合版本的程序采用了与 C 版本相同的算法，包括基于分裂步 Crank-Nicolson 方法的实部和虚部传播，但仅考虑完全各向异性的三维 GP 方程。由于大网格尺寸的算法复杂性，为了减少执行时间及/或每个节点的内存需求，必须进行并行化。鉴于需要分布式内存方法来解决上述问题，我们将 MPI 编程范式与现有的 OpenMP 代码相结合，从而在结合的分布式/共享内存模型中实现完全灵活的并行性，适用于不同的现代计算机架构。所提供的两个用于实部和虚部传播的 C/OpenMP/MPI 程序经过优化，并附有可定制的 makefile。我们展示了所提供的 OpenMP/MPI 代码的典型可扩展性结果，并证明了在进程间通信时间开始主导每次迭代的计算时间之前，几乎实现了线性加速。对于大网格尺寸，此类可扩展性研究是必要的，以便确定最佳 MPI 节点数和每个节点的 OpenMP 线程数。

此程序的先前版本（AEDU_v1_0 和 AEDU_v2_0）可在 dx.doi.org/10.1016/j.cpc.2009.04.015 和 dx.doi.org/10.1016/j.cpc.2012.03.022 分别找到。该数据集原始版本（http://dx.doi.org/10.17632/hrk84bznv2.1）中的一个源文件存在错别字，已在当前版本中更正。