  We propose a sparse grids based adaptive noise reduction strategy for
electrostatic particle-in-cell (PIC) simulations. Our approach is based on the
key idea of relying on sparse grids instead of a regular grid in order to
increase the number of particles per cell for the same total number of
particles, as first introduced in Ricketson and Cerfon (Plasma Phys. and
Control. Fusion, 59(2), 024002). Adopting a new filtering perspective for this
idea, we construct the algorithm so that it can be easily integrated into high
performance large-scale PIC code bases. Unlike the physical and Fourier domain
filters typically used in PIC codes, our approach automatically adapts to mesh
size, number of particles per cell, smoothness of the density profile and the
initial sampling technique. Thanks to the truncated combination technique, we
can reduce the larger grid-based error of the standard sparse grids approach
for non-aligned and non-smooth functions. We propose a heuristic based on
formal error analysis for selecting the optimal truncation parameter at each
time step, and develop a natural framework to minimize the total error in
sparse PIC simulations. We demonstrate its efficiency and performance by means
of two test cases: the diocotron instability in two dimensions, and the
three-dimensional electron dynamics in a Penning trap. Our run time performance
studies indicate that our new scheme can provide significant speedup and memory
reduction as compared to regular PIC for achieving comparable accuracy in the
charge density deposition.
