Speeding up N body simulations of modified gravity: chameleon screening models
Abstract
We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard NewtonGaussSeidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512{sup 3} particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millenniumresolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running verymore »
 Authors:
 Institute for Computational Cosmology, Department of Physics, Durham University, Durham DH1 3LE (United Kingdom)
 MaxPlanckInstitut für Astrophysik, KarlSchwarzschildStr. 1, 85741 Garching (Germany)
 Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom)
 National Astronomy Observatories, Chinese Academy of Science, Beijing, 100012 (China)
 Publication Date:
 OSTI Identifier:
 22680005
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 02; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; COMPUTERIZED SIMULATION; CONVERGENCE; EFFICIENCY; GRAVITATION; INSTABILITY; ITERATIVE METHODS; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; PERFORMANCE; RESOLUTION; STANDARD MODEL; VELOCITY
Citation Formats
Bose, Sownak, Li, Baojiu, He, Jianhua, Llinares, Claudio, Barreira, Alexandre, Hellwing, Wojciech A., Koyama, Kazuya, and Zhao, GongBo, Email: sownak.bose@durham.ac.uk, Email: baojiu.li@durham.ac.uk, Email: barreira@mpagarching.mpg.de, Email: jianhua.he@durham.ac.uk, Email: wojciech.hellwing@port.ac.uk, Email: kazuya.koyama@port.ac.uk, Email: claudio.llinares@durham.ac.uk, Email: gbzhao@nao.cas.cn. Speeding up N body simulations of modified gravity: chameleon screening models. United States: N. p., 2017.
Web. doi:10.1088/14757516/2017/02/050.
Bose, Sownak, Li, Baojiu, He, Jianhua, Llinares, Claudio, Barreira, Alexandre, Hellwing, Wojciech A., Koyama, Kazuya, & Zhao, GongBo, Email: sownak.bose@durham.ac.uk, Email: baojiu.li@durham.ac.uk, Email: barreira@mpagarching.mpg.de, Email: jianhua.he@durham.ac.uk, Email: wojciech.hellwing@port.ac.uk, Email: kazuya.koyama@port.ac.uk, Email: claudio.llinares@durham.ac.uk, Email: gbzhao@nao.cas.cn. Speeding up N body simulations of modified gravity: chameleon screening models. United States. doi:10.1088/14757516/2017/02/050.
Bose, Sownak, Li, Baojiu, He, Jianhua, Llinares, Claudio, Barreira, Alexandre, Hellwing, Wojciech A., Koyama, Kazuya, and Zhao, GongBo, Email: sownak.bose@durham.ac.uk, Email: baojiu.li@durham.ac.uk, Email: barreira@mpagarching.mpg.de, Email: jianhua.he@durham.ac.uk, Email: wojciech.hellwing@port.ac.uk, Email: kazuya.koyama@port.ac.uk, Email: claudio.llinares@durham.ac.uk, Email: gbzhao@nao.cas.cn. Wed .
"Speeding up N body simulations of modified gravity: chameleon screening models". United States.
doi:10.1088/14757516/2017/02/050.
@article{osti_22680005,
title = {Speeding up N body simulations of modified gravity: chameleon screening models},
author = {Bose, Sownak and Li, Baojiu and He, Jianhua and Llinares, Claudio and Barreira, Alexandre and Hellwing, Wojciech A. and Koyama, Kazuya and Zhao, GongBo, Email: sownak.bose@durham.ac.uk, Email: baojiu.li@durham.ac.uk, Email: barreira@mpagarching.mpg.de, Email: jianhua.he@durham.ac.uk, Email: wojciech.hellwing@port.ac.uk, Email: kazuya.koyama@port.ac.uk, Email: claudio.llinares@durham.ac.uk, Email: gbzhao@nao.cas.cn},
abstractNote = {We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard NewtonGaussSeidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512{sup 3} particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millenniumresolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, largesized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.},
doi = {10.1088/14757516/2017/02/050},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 02,
volume = 2017,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}

We introduce and demonstrate the power of a method to speed up current iterative techniques for Nbody modified gravity simulations. Our method is based on the observation that the accuracy of the final result is not compromised if the calculation of the fifth force becomes less accurate, but substantially faster, in highdensity regions where it is relatively weak due to screening. We focus on the nDGP model which employs Vainshtein screening, and test our method by running AMR simulations in which the fifth force on the finer levels of the mesh (high density) is not obtained iteratively, but instead interpolatedmore »

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