A massively parallel semi-Lagrangian solver for the six-dimensional Vlasov-Poisson equation

Abstract

This paper presents an optimized and scalable semi-Lagrangian solver for the Vlasov-Poisson system in six-dimensional phase space. Grid-based solvers of the Vlasov equation are known to give accurate results. At the same time, these solvers are challenged by the curse of dimensionality resulting in very high memory requirements, and moreover, requiring highly efficient parallelization schemes. In this paper, we consider the 6d Vlasov-Poisson problem discretized by a split-step semi-Lagrangian scheme, using successive 1d interpolations on 1d stripes of the 6d domain. Two parallelization paradigms are compared, a remapping scheme and a classical domain decomposition approach applied to the full 6d problem. From numerical experiments, the latter approach is found to be superior in the massively parallel case in various respects. We address the challenge of artificial time step restrictions due to the decomposition of the domain by introducing a blocked one-sided communication scheme for the purely electrostatic case and a rotating mesh for the case with a constant magnetic field. In addition, we propose a pipelining scheme that enables to hide the costs for the halo communication between neighbor processes efficiently behind useful computation. Parallel scalability on up to 65k processes is demonstrated for benchmark problems on a supercomputer.

References in corpus (10)

• Dual phase-space cascades in 3D hybrid-Vlasov-Maxwell turbulence
• A semi-Lagrangian Vlasov solver in tensor train format
• Fully kinetic versus reduced-kinetic modelling of collisionless plasma turbulence
• Direct Integration of the Collisionless Boltzmann Equation in Six-dimensional Phase Space: Self-gravitating Systems
• Comparison of time splitting and backsubstitution methods for integrating Vlasov's equation with magnetic fields
• Multidimensional VlasovPoisson Simulations with High-order Monotonicity- and Positivity-preserving Schemes
• A dynamical adaptive tensor method for the Vlasov-Poisson system
• A portable platform for accelerated PIC codes and its application to GPUs using OpenACC
• Verification of nonlinear particle simulation of radio frequency waves in tokamak
• Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection. I: Macroscopic effects of the electron flows

Cited by in corpus (11)

• A quantum-inspired method for solving the Vlasov-Poisson equations
• A Parallel Low-Rank Solver for the Six-Dimensional Vlasov-Maxwell Equations
• Investigating the use of field solvers for simulating classical systems
• An Energy Conserving Vlasov Solver That Tolerates Coarse Velocity Space Resolutions: Simulation of MMS Reconnection Events
• Importance of accurate consideration of the electron inertia in hybrid-kinetic simulations of collisionless plasma turbulence: 1. The 2D limit
• High frequency non-gyrokinetic turbulence at tokamak edge parameter
• A mass-conserving sparse grid combination technique with biorthogonal hierarchical basis functions for kinetic simulations
• Convergence of splitting methods on rotating grids for the magnetized Vlasov equation
• Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
• Local cubic spline interpolation for Vlasov-type equations on a multi-patch geometry
• An efficient stochastic particle method for high-dimensional nonlinear PDEs