Charge-conserving gather-scatter algorithm for PIC simulations on unstructured grids

A novel charge-conserving gather-scatter algorithm for particle-in-cell (PIC) simulations on unstructured grids is presented. The algorithm exactly preserves charge conservation, so additional correction terms are not needed. It is inspired by the exterior calculus of differential forms and on the use of Whitney forms as interpolants for both current and charge deposition onto the grid. The charge conservation is verified without the need for any shape factors and independently of time integration scheme used for the determination of current density.