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N-body simulations are essential tools in physical cosmology to understand the large-scale structure (LSS) formation of the Universe. Large-scale simulations with high resolution are important for exploring the substructure of universe and for determining fundamental physical parameters like neutrino mass. However, traditional particle-mesh (PM) based algorithms use considerable amounts of memory, which limits the scalability of simulations. Therefore, we designed a two-level PM algorithm CUBE towards optimal performance in memory consumption reduction. By using the fixed-point compression technique, CUBE reduces the memory consumption per N-body particle toward 6 bytes, an order of magnitude lower than the traditional PM-based algorithms. We scaled CUBE to 512 nodes (20,480 cores) on an Intel Cascade Lake based supercomputer with $simeq$95% weak-scaling efficiency. This scaling test was performed in Cosmo-$pi$ -- a cosmological LSS simulation using $simeq$4.4 trillion particles, tracing the evolution of the universe over $simeq$13.7 billion years. To our best knowledge, Cosmo-$pi$ is the largest completed cosmological N-body simulation. We believe CUBE has a huge potential to scale on exascale supercomputers for larger simulations.
Cosmological large scale structure $N$-body simulations are computation-light, memory-heavy problems in supercomputing. The considerable amount of memory is usually dominated by an inefficient way of storing more than sufficient phase space informati
Gravitational softening length is one of the key parameters to properly set up a cosmological $N$-body simulation. In this paper, we perform a large suit of high-resolution $N$-body simulations to revise the optimal softening scheme proposed by Power
We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the synchronous-comoving gau
(Abridged) We use high resolution cosmological N-body simulations to study the growth of intermediate to supermassive black holes from redshift 49 to zero. We track the growth of black holes from the seeds of population III stars to black holes in th
Simulations of galaxy formation follow the gravitational and hydrodynamical interactions between gas, stars and dark matter through cosmic time. The huge dynamic range of such calculations severely limits strong scaling behaviour of the community cod