A 400 Trillion-Grid Vlasov Simulation on Fugaku Supercomputer:
  Large-Scale Distribution of Cosmic Relic Neutrinos in a Six-dimensional Phase
  Space
  We report a Vlasov simulation of cosmic relic neutrinos combined with N-body
simulation of cold dark matter in the context of large-scale structure
formation in the Universe performed on Fugaku supercomputer. Gravitational
dynamics of the neutrinos is followed, for the first time, by directly
integrating the Vlasov equation in a six-dimensional phase space. Our largest
simulation combines the Vlasov simulation on 400 trillion grids and 330
billion-body calculations in a self-consistent manner, and reproduces
accurately the nonlinear dynamics of neutrinos in the Universe. The novel
high-order Vlasov solver is optimized by combining an array of state-of-the-art
numerical schemes and fully utilizing the SIMD instructions on the A64FX
processors. Time-To-Solution of our simulation is an order of magnitude shorter
than the largest N-body simulations. The performance scales excellently with up
to 147,456 nodes (7 million CPU cores) on Fugaku; the weak and strong scaling
efficiencies are 82% - 96% and 82% - 93%, respectively.
