  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 NNLO$_{\rm opt}$ 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 at scattering energies
$0-350$ MeV in the laboratory frame of reference. Considering only scattering
energies $\sim40-350$ MeV, we find a smaller method error of $\lesssim 1-2$ 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, a
GPU-implementation is mainly advantageous for matrices that fit in the fast
on-chip shared memory. We find that WPCD is a promising method for
computationally efficient, statistical analyses of nuclear interactions from
effective field theory, where we can utilise Bayesian inference methods to
incorporate relevant uncertainties.
