Vector functions for singular fields on curved triangular elements, truly defined in the parent space

This paper presents singular curl- and divergence-conforming functions of interpolative kind on curved triangular elements, directly defined in their parent triangle of area coordinates (ξ₁ξ_2; ξ₃=1-ξ₁-ξ₂), without introducing any intermediate (polar) reference frame as previously done in other works. Curl-conforming functions are useful in the FEM solution of the transverse vector Helmholtz equation, whereas divergence-conforming functions are used in the moments method solution of surface integral equations. Singular vector functions for hierarchical families are easily extracted from those given here. Our functions incorporate the edge condition and are able to approximate the unknown field components in the neighborhood of the edge of a wedge for any order of the singularity coefficient υ, that is supposed given and known a priori. The wedge can be penetrable in the curl-conforming case, while it is supposed metallic in the divergence conforming case.