Sparse grid reconstructions for Particle-In-Cell methods

In this article, we propose and analyse Particle-In-Cell (PIC) methods embedding sparse grid reconstructions such as those introduced in Ricketson Cerfon [ Plasma Phys. Control. Fusion 59 (2017) 024002] Muralikrishnan et al . J. Comput. X 11 (2021) 100094]. The offer a significant improvement on the statistical error of PIC schemes well reduction complexity problem providing electric field. Main results convergence field interpolant conservation properties are provided paper. Besides, tailored reconstructions, frame offset combination technique, proposed to introduce with improved efficiency. assessed numerically compared existing thanks classical benchmarks remarkable prospects for three dimensional computations.