A High-Fidelity Realization of the Euclid Code Comparison $N$-body Simulation with Abacus

We present a high-fidelity realization of the cosmological $N$-body simulation from the Schneider et al. (2016) code comparison project. The simulation was performed with our Abacus $N$-body code, which offers high force accuracy, high performance, and minimal particle integration errors. The simulation consists of ${2048}^3$ particles in a $500h^{-1}\mathrm{M}\mathrm{p}\mathrm{c}$ box, for a particle mass of $1.2\times {10}^9{h}^{-1}{\mathrm{M}}_{\odot }$ with $10
h^{-1}$\mathrm{k}\mathrm{p}\mathrm{c}$$splinesoftening\mathrm{.}Abacusexecuted1052globaltimestepsto$z=0$ in 107 hours on one dual-Xeon, dual-GPU node, for a mean rate of 23 million particles per second per step. We find Abacus is in good agreement with Ramses and Pkdgrav3 and less so with Gadget3. We validate our choice of time step by halving the step size and find sub-percent differences in the power spectrum and 2PCF at nearly all measured scales, with $<0.3\mathrm{\%}$ errors at $k<10
$\mathrm{M}\mathrm{p}\mathrm{c}$^{-1}h$. On large scales, Abacus reproduces linear theory better than $0.01\mathrm{\%}$. Simulation snapshots are available at http://nbody.rc.fas.harvard.edu/public/S2016 .