Perfectly parallel cosmological simulations using spatial comoving Lagrangian acceleration

¹ Imperial Centre for Inference and Cosmology (ICIC) & Astrophysics Group, Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK
e-mail: florent.leclercq@polytechnique.org
² AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
³ CNRS, Sorbonne Université, UMR 7095, Institut d’Astrophysique de Paris, 98bis bd Arago, 75014 Paris, France
⁴ Sorbonne Université, Institut Lagrange de Paris (ILP), 98 bis bd Arago, 75014 Paris, France
⁵ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010 New York, NY, USA
⁶ Waterloo Centre for Astrophysics, University of Waterloo, 200 University Ave W, Waterloo ON N2L 3G1, Canada
⁷ Department of Physics and Astronomy, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada
⁸ Perimeter Institute for Theoretical Physics, 31 Caroline St. North, Waterloo ON N2L 2Y5, Canada

Received: 20 March 2020
Accepted: 15 May 2020

Abstract

Context. Existing cosmological simulation methods lack a high degree of parallelism due to the long-range nature of the gravitational force, which limits the size of simulations that can be run at high resolution.

Aims. To solve this problem, we propose a new, perfectly parallel approach to simulate cosmic structure formation, which is based on the spatial COmoving Lagrangian Acceleration (sCOLA) framework.

Methods. Building upon a hybrid analytical and numerical description of particles’ trajectories, our algorithm allows for an efficient tiling of a cosmological volume, where the dynamics within each tile is computed independently. As a consequence, the degree of parallelism is equal to the number of tiles. We optimised the accuracy of sCOLA through the use of a buffer region around tiles and of appropriate Dirichlet boundary conditions around sCOLA boxes.

Results. As a result, we show that cosmological simulations at the degree of accuracy required for the analysis of the next generation of surveys can be run in drastically reduced wall-clock times and with very low memory requirements.

Conclusions. The perfect scalability of our algorithm unlocks profoundly new possibilities for computing larger cosmological simulations at high resolution, taking advantage of a variety of hardware architectures.