Four cheap improvements to the particle-mesh code

Abstract

The two dimensional electrostatic particle-mesh code is improved in four ways at no significant cost in computation. The exact spectrum of the potential periodic in both κ- and real space is derived. The particle shape is adjusted to reduce the dependence of the particle potential on the mesh position. Field errors are halved by using a mesh offset from that used during the charge assignment. Non-central forces are reduced by a factor typically about 10 by modifying the spectrum. © 1981.