Sparse grid techniques for particle-in-cell schemes

Abstract

We propose the use of sparse grids to accelerate particlein-cell (PIC) schemes. By using the so-called 'combination technique' from the sparse grids literature, we are able to dramatically increase the size of the spatial cells in multi-dimensional PIC schemes while paying only a slight penalty in grid-based error. The resulting increase in cell size allows us to reduce the statistical noise in the simulation without increasing total particle number. We present initial proof-of-principle results from test cases in two and three dimensions that demonstrate the new scheme's efficiency, both in terms of computation time and memory usage. arXiv:1607.06516v1 [physics.comp-ph]

Efficient Strict-Binning Particle-in-Cell Algorithm for Multi-core SIMD Processors

“…We consider a classical Landau-damping test case [3,11], simulating 2 billion particles on a 64×64×64 grid, for 500 time steps. We use the same parameters as in [18]: time step of 0.05, periodic boundary conditions on spatial domain Ω = [0, 22] 3 and initial distribution function:…”

Application of sparse grid combination techniques to low temperature plasmas particle-in-cell simulations. I. Capacitively coupled radio frequency discharges

“…Following the formal analysis conducted by Ricketson and Cerfon [35] a sparse grid approximation of charge density , ( denoting the particle species) may be reconstructed on the regular grid using Eq. (1):…”

“…We have hence adopted a different strategy (also detailed in ref. [35]) to benefit from the advantage of the sparse grid combination technique by resolving Poisson's equation on each of the 2 − 1 sub-grids (2 − 1 corresponding to the total number of sub-grids that are constructed from a depth in the maximum-norm based grid). Due to the reduction of the size of linear systems solved on each of the sparse grids, a substantial gain in numerical efficiency is achieved.…”

“…Applying sparse PIC techniques in the context of capacitive discharges allows us to explore the potentiality and the limits of the method when sheaths are present (this not done in Ref. [35]). The capacitive coupled discharges also offer the opportunity to test boundary conditions varying in time, and collisions (including ionization to self-sustain the discharge).…”

“…This number grows in 2D and 3D so that the total number of particles can become large enough to exceed the maximum memory resources available on the even most performant computers. Ricketson and Cerfon have proposed to apply the so called "sparse grid" combination method to accelerate PIC simulations by reducing the number of cells in the simulation domain and consequently the total number of macroparticles [35]. An increase of the grid cell sizes allows to reduce the statistical noise in the simulation without increasing the total particle number They have verified this new approach with three benchmarking tests encountered in plasma physics (linear and nonlinear landau damping in 3D and diocotron instability in 2D).…”