GPU-accelerated time integration of Gross-Pitaevskii equation with discrete exterior calculus

Abstract

The quantized vortices in superfluids are modeled by the Gross-Pitaevskii equation whose numerical time integration is instrumental in the physics studies of such systems. In this paper, we present a reliable numerical method and its efficient GPU-accelerated implementation for the time integration of the three-dimensional Gross-Pitaevskii equation. The method is based on discrete exterior calculus which allows us the usage of more versatile spatial discretization than traditional finite difference and spectral methods are applicable to. We discretize the problem using six different natural crystal structures and observe the correct choices of spatial tiling to decrease the truncation error and increase the reliability compared to Cartesian grids. We pay attention to the computational performance optimizations of the GPU implementation and measure speedups of up to 152-fold when compared to a reference CPU implementation. We parallelize the implementation further to multiple GPUs and show that 92% of the computation time can fully utilize the additional resources.