Step-Like Structures in Electrostatic and Electrodynamic Implementation of Method of Moments: Some Unique Observations

Step-like perfect electric conductor (PEC) structures are studied in both electrostatic and electrodynamic cases implementing Method of Moments. The canonical geometries included in these step-like structures such as edges, wedges and corners as well as the unique charge and current behaviors are characterized and discussed. Both 2D and 3D electrostatic problems are studied. In 2D electrostatic problem, a constant is introduced to the traditional 2D Green’s function which effectively adjusts the zero potential reference embedded in the Green’s function. This modification alleviates the contradiction between 2D and 3D definitions of electrostatic quantities and avoids unrealistic charge solutions obtained by Method of Moments. In 2D electrodynamic problem, the occasional appearance of singular surface current near the step’s right angle bends is observed, discussed and then linked with the analytical solution of a canonical wedge scattering problem. Physical Optics approximation is also utilized as a comparison to Method of Moments in solving the 2D scattering problems. © Wang and Rahmat-Samii