Controlling self-force errors at refinement boundaries for AMR-PIC

We analyze the source of the self-force errors in the node-centered adaptive-mesh-refinement particle-in-cell (AMR-PIC) algorithm and propose a method for reducing those self-forces. Our approach is based on a method of charge deposition due to Mayo [A. Mayo, The fast solution of Poisson’s and the biharmonic equations on irregular regions, SIAM Journal of Numerical Analysis 21(2) (1984) 285–299] that can reduce the self-force error to any specified degree of accuracy.