Accelerating Nucleon-Nucleon Scattering Calculations: https://arxiv.org/abs/2106.00454
Sean B. S. Miller, Andreas Ekström, Christian Forssén
In this paper we analyse the efficiency, precision, and accuracy of computing elastic nucleon-nucleon (NN) scattering amplitudes with the wave-packet continuum discretisation method (WPCD). This method provides approximate scattering solutions at multiple scattering energies simultaneously. We therefore utilise a graphics processing unit (GPU) to explore the benefits of this inherent parallelism. From a theoretical perspective, the WPCD method promises a speedup compared to a standard matrix-inversion method. We use the chiral NNLOopt interaction to demonstrate that WPCD enables efficient computation of NN scattering amplitudes provided one can tolerate an averaged method error of 1−5 mb in the total cross section. For scattering energies ≳40 MeV, in the laboratory frame of reference, we find a much smaller method error of ≲1 mb. By increasing the number of wave-packets we can further reduce the overall method error. However, the parallel leverage of the WPCD method will be offset by the increased size of the resulting discretisation mesh. In practice, the GPU implementation is only useful for matrices that fit in the fast on-chip shared memory. Nevertheless, we find that WPCD is a promising method for computationally efficient, statistical analyses of EFT nuclear interactions, where we can utilise Bayesian inference methods to incorporate relevant uncertainties.
Comments: 17 pages, 9 figures