Additive singular high-order complete vector functions for FEM and MoM applications to 2D and 3D sharp-wedge structures

The paper summarizes the research results obtained on numerical modeling of the diffraction effects due to abrupt material or geometrical discontinuities of electromagnetic structures. High order polynomial vector bases are often used to numerically model EM problems, but polynomial approximations spoil the convergence properties of the used finite method whenever the physical quantities have singular and/or irrational algebraic behavior in wedge regions. Our specially derived sub-sectional singular curl- and divergence-conforming vector bases incorporate the edge conditions of penetrable or conducting wedges, and yields to high precision results without requiring the use of dense meshes and/or local mesh refinements.