Compatible Singular Vector Functions For Computational Electromagnetics

The research work done by several authors in order to incorporate the edge conditions in the numerical solution of electromagnetic problems is reviewed by considering the development of singular vector expansion functions for the Method of Moments solution of integral equations and for the Finite Element Method solution of partial differential equations. The paper then presents new singular curl- and divergence-conforming functions of interpolative kind on curved triangular elements, directly defined in their parent triangle, without resorting to an intermediate (polar) reference frame as previous works did. The new curl (divergence) conforming singular functions provided here are compatible with standard zero-order vector functions in adjacent elements and guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modelling of the curl (divergence), and removal of spurious modes (solutions).