Singular Tetrahedral Finite Elements for Vector Electromagnetics

The electromagnetic fields at reentrant edges made of conductor are generally singular and the polynomial basis functions used in traditional finite elements do not model the fields well in these regions. Two new tetrahedral elements are introduced with basis functions that incorporate the known asymptotic variation of the fields with distance from the edge. The basis is split into gradient and rotational parts. Additional vertex functions can be added to improve the conditioning of the global matrix system that arises in the time-harmonic case. Results are presented for the scattering parameters of a number of waveguide discontinuities. The new elements reduce the error considerably compared to the Whitney element, and generally outperform the second-order edge element, even though that has more degrees of freedom