skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation

Abstract

Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuationmore » composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.« less

Authors:
 [1];  [2];  [2];  [1];  [2]
  1. Institut d'Astrophysique de Paris, CNRS UMR 7095 and UPMC, 98bis, bd Arago, F-75014 Paris (France)
  2. (Japan)
Publication Date:
OSTI Identifier:
22572354
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 321; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CHAOS THEORY; COSMOLOGY; EQUATIONS OF MOTION; HAMILTONIANS; LAGRANGIAN FUNCTION; NONLUMINOUS MATTER; PHASE SPACE; POISSON EQUATION; POTENTIALS; SHEETS; SIMULATION

Citation Formats

Sousbie, Thierry, E-mail: tsousbie@gmail.com, Department of Physics, The University of Tokyo, Tokyo 113-0033, Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033, Colombi, Stéphane, E-mail: colombi@iap.fr, and Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502. ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation. United States: N. p., 2016. Web. doi:10.1016/J.JCP.2016.05.048.
Sousbie, Thierry, E-mail: tsousbie@gmail.com, Department of Physics, The University of Tokyo, Tokyo 113-0033, Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033, Colombi, Stéphane, E-mail: colombi@iap.fr, & Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502. ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation. United States. doi:10.1016/J.JCP.2016.05.048.
Sousbie, Thierry, E-mail: tsousbie@gmail.com, Department of Physics, The University of Tokyo, Tokyo 113-0033, Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033, Colombi, Stéphane, E-mail: colombi@iap.fr, and Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502. 2016. "ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation". United States. doi:10.1016/J.JCP.2016.05.048.
@article{osti_22572354,
title = {ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation},
author = {Sousbie, Thierry, E-mail: tsousbie@gmail.com and Department of Physics, The University of Tokyo, Tokyo 113-0033 and Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033 and Colombi, Stéphane, E-mail: colombi@iap.fr and Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502},
abstractNote = {Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.},
doi = {10.1016/J.JCP.2016.05.048},
journal = {Journal of Computational Physics},
number = ,
volume = 321,
place = {United States},
year = 2016,
month = 9
}
  • We present a direct, adaptive solver for the Poisson equation which can achieve any prescribed order of accuracy. It is based on a domain decomposition approach using local spectral approximation, as well as potential theory and the fast multipole method. In two space dimensions, the algorithm requires O(NK) work, where N is the number of discretization points and K is the desired order of accuracy. 32 refs., 6 figs., 4 tabs.
  • A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: themore » algorithms, the implementation and the usage.« less
  • The Adaptive Poisson-Boltzmann Solver (APBS) is a state-of-the-art suite for performing Poisson-Boltzmann electrostatic calculations on biomolecules. The iAPBS package provides a modular programmatic interface to the APBS library of electrostatic calculation routines. The iAPBS interface library can be linked with a Fortran or C/C++ program thus making all of the APBS functionality available from within the application. Several application modules for popular molecular dynamics simulation packages -- Amber, NAMD and CHARMM are distributed with iAPBS allowing users of these packages to perform implicit solvent electrostatic calculations with APBS.
  • This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numericalmore » results.« less