OpenMP, OpenMP/MPI, and CUDA/MPI C programs for solving the time-dependent dipolar Gross-Pitaevskii equation

TL;DR

This paper introduces improved, parallelized C and CUDA programs for solving the dipolar Gross-Pitaevskii equation across multiple dimensions, demonstrating significant speedups on various hardware configurations.

Contribution

The paper develops and compares new OpenMP, MPI, and CUDA/MPI parallelized programs for the dipolar Gross-Pitaevskii equation, enhancing computational efficiency over previous versions.

Findings

Sequential program speedup of 1.1 to 1.9

OpenMP parallelization speedup of 2 to 12

MPI/MPI and CUDA/MPI versions achieve 9 to 16.5 speedup on clusters

Abstract

We present new versions of the previously published C and CUDA programs for solving the dipolar Gross-Pitaevskii equation in one, two, and three spatial dimensions, which calculate stationary and non-stationary solutions by propagation in imaginary or real time. Presented programs are improved and parallelized versions of previous programs, divided into three packages according to the type of parallelization. First package contains improved and threaded version of sequential C programs using OpenMP. Second package additionally parallelizes three-dimensional variants of the OpenMP programs using MPI, allowing them to be run on distributed-memory systems. Finally, previous three-dimensional CUDA-parallelized programs are further parallelized using MPI, similarly as the OpenMP programs. We also present speedup test results obtained using new versions of programs in comparison with the previous sequential C and parallel CUDA programs. The improvements to the sequential version yield a speedup of 1.1 to 1.9, depending on the program. OpenMP parallelization yields further speedup of 2 to 12 on a 16-core workstation, while OpenMP/MPI version demonstrates a speedup of 11.5 to 16.5 on a computer cluster with 32 nodes used. CUDA/MPI version shows a speedup of 9 to 10 on a computer cluster with 32 nodes.