Note on the use of Yee-lattices in (semi-) implicit Particle-in-cell   codes
  A modification of the implicit algorithm for particle-in-cell simulations proposed by Petrov and Davis [2011] is presented. The original lattice arrangement is not inherently divergence-free, possibly leading to unphysical results. This arrangement is replaced by a staggered mesh resulting in a reduction of the divergence of the magnetic field by several orders of magnitude. 
Andreas Kempf, Urs Ganse, Patrick Kilian, Felix Spanier
physics.comp-ph physics.plasm-ph