Generalized Poisson-Neumann polygonal basis functions for the electromagnetic simulation of complex planar structures

Rooftop functions are commonly used for the discretization of planar currents in electromagnetic (EM) simulators. We describe the generalization of the rectangular and triangular rooftop functions to arbitrary polygonally shaped subdomains. It is shown that these generalized basis functions are solutions to a pertinent Neumann-Poisson problem, and we derive the integral equations satisfied by these basis functions. The new generalized polygonal functions allow for a more efficient meshing of complex geometrical structures in terms of polygonally shaped cells. They naturally model the current flow in the polygonal cells, satisfy the current continuity relation, and significantly enhance the EM simulation performance for complex geometrical structures. The increased simulation performance is demonstrated for a complex radio-frequency board interconnection layout and a spiral inductor on a silicon substrate.