Sparse grid techniques for particle-in-cell schemes

TL;DR

This paper introduces a novel approach using sparse grid techniques to enhance particle-in-cell simulations, significantly reducing noise and computational resources while maintaining accuracy in multi-dimensional plasma modeling.

Contribution

The paper presents a new method applying sparse grids and the combination technique to accelerate PIC schemes, enabling larger cells and reduced noise with minimal error increase.

Findings

Significant reduction in statistical noise in PIC simulations.

Improved computational efficiency and memory usage.

Proof-of-principle results in 2D and 3D demonstrating effectiveness.

Abstract

We propose the use of sparse grids to accelerate particle-in-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.