混合OpenMP/MPI程序求解完全各向异性陷阱中的含时Gross-Pitaevskii方程
Hybrid OpenMP/MPI programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
摘要：
我们提出了混合的OpenMP/MPI（开放多处理/消息传递接口）并行版本的早期出版的C程序（D。Vudragovic等人，Comput.物理通讯183，2021（2012）），用于计算三维空间中的时间相关的Gross-Pitaevskii（GP）方程的稳态和非稳态解。GP方程描述了超低温下稀玻色-爱因斯坦凝聚体的性质。混合版本的程序使用与C相同的算法，包括基于分步Crank-Nicolson方法的实时和实时传播，但只考虑完全各向异性的三维GP方程，其中大网格尺寸的算法复杂性需要并行化，以减少每个节点的执行时间和/或内存需求。由于分布式内存的方法是需要解决后者，我们结合MPI编程范式与现有的OpenMP代码，从而创建一个组合的分布式/共享内存模型，适合于不同的现代计算机体系结构的完全灵活的并行性。两个提出的C/OpenMP/MPI程序的实时和非实时传播进行了优化，并伴随着一个可定制的makefile。我们提出了典型的可扩展性结果提供的OpenMP/MPI代码，并证明几乎线性加速，直到进程间的通信时间开始占主导地位，每次迭代的计算时间。这样的可扩展性研究是必要的大网格大小，以确定最佳的MPI节点和每个节点的OpenMP线程数。
英文摘要：
We present hybrid OpenMP/MPI (Open Multi-Processing/Message Passing Interface) parallelized versions of earlier published C programs (D. Vudragovic et al., Comput. Phys. Commun. 183, 2021 (2012)) 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.
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