Numerical differentiation of Laplacian 3-D FE solutions by using regular polyhedra quadrature of Poisson integrals

An efficient numerical procedure to compute accurately derivatives of three-dimensional (3-D) Finite Element (FE) solutions to Laplacian electromagnetic problems is presented. The technique adopted is based on the combined use of Poisson Integrals and an innovative quadrature approach, exploiting symmetry properties by using as integration points vertices of regular polyhedra. The postprocessing procedure gets highly accurate results with a modest computational effort if compared with standard integration techniques. It has been found by comparison against known analytical functions that only few points are needed to reach a high degree of accuracy