Extended Multi-branch basis functions for non-conformal problems

Discontinuous Galerkin (DG) approaches [1] used to connect two non-conformal surfaces in the Method of Moments typical employ Interior Penalty (IP) methods to mitigate charge accumulation along the half RWG basis functions connection boundary. These IP approaches are introduced via a combined impedance matrix $(Z-\beta$. $I P$). Alternatively in soft non-conforming problems, Multi-branch (MB-RWG) basis functions can be utilized [2]. Generalizations of multibranch basis functions can lead to higher degress of nonconformality as the use of $N^{+}-N^{-}$ branches MB_RWG [3] when $N^{+}$ and $N^{-}$ triangles have common vertices at the endpoints of the shared countour, but not along the contour.