Postprocessing of 3-D static-field FE solutions by using regular polyhedra quadrature of Poisson integrals

A new quadrature approach is illustrated for the accurate numerical computation of Poisson integrals used in postprocessing of three-dimensional (3-D) finite-element (FE) solutions to Poisson equations. The innovative quadrature formulas, which exploit geometrical properties of regular polyhedra, are very easy to implement and allow us to obtain accurate results with a lower computational cost with respect to traditional quadrature techniques. Accuracy tests are presented, showing comparisons against both analytical and numerical results. An example of postprocessing of some FE solutions concerning the steady-state 3-D electromagnetic analysis of a real vacuum electron device is also given to better illustrate the advantages of the presented procedure.