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

TL;DR

This paper introduces hybrid OpenMP/MPI parallelized C programs for efficiently solving the 3D time-dependent Gross-Pitaevskii equation, enabling scalable simulations of Bose-Einstein condensates on modern computer architectures.

Contribution

It develops and optimizes hybrid OpenMP/MPI programs for the 3D Gross-Pitaevskii equation, combining distributed and shared memory parallelism for improved scalability.

Findings

Almost linear speedup achieved with increasing MPI nodes and OpenMP threads

Scalability results demonstrate efficient parallelization for large grid sizes

Optimized, customizable code suitable for modern high-performance computing architectures

Abstract

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.