Overrelaxing the charge iteration procedure

Charge iteration is an N-dimensional (N=1,2,3) FEM procedure for the solution of unbounded electrostatic fields created by voltaged conductors. In the procedure a fictitious boundary enclosing all the conductors defines a bounded region where the unbounded problem is solved iteratively using the charge lying on conductors to improve the Dirichlet condition on the fictitious boundary. The convergence properties of charge iteration in the presence of overrelaxation are investigated. A remarkable reduction in computational effort is obtained due to the reduction in the number of iterations and the restriction of the bounded domain to the vicinity of the conductors where the unrelaxed procedure exhibits a divergent behaviour. The above advantages are illustrated by an analytical verification and by a numerical example.