Interfacing the finite-element method with the method of characteristics in self-consistent electrostatic field models

Two methods are described for interfacing the finite-element method, used to calculate the electric field structure for a known charge distribution, with the method of characteristics, used to calculate the charge distribution for a known electric field structure, so as to obtain self-consistent descriptions of electrostatic systems involving two-way source-field coupling. Both methods circumvent difficulties which have limited application of the finite-element method of characteristics methodology in the past. One method involves automatic retriangulation, based upon the Delaunay algorithm, on each source-field iteration, using finite-element nodes lying directly upon characteristic lines. The other method involves projection of characteristic lines back through a fixed finite-element mesh to their initiation points on the injection electrode. Both methods make use of second-order potential variations within finite elements and thus involve curved characteristic trajectories within each element. Results of each method are compared with those of previous work on self consistent source-field coupling