Differential-Forms-Motivated Discretizations of Electromagnetic Differential and Integral Equations

In this letter, we present a differential-forms-motivated procedure to unify and guide discretizations of differential and integral equations in computational electromagnetics (CEM). In order to solve such equations accurately, it is crucial to find an appropriate matrix representation of the governing differential or integral operator. Differential forms theory inspires a general procedure of selecting both expansion and test functions wisely. Many well-functioning discretizations in finite element method (FEM) and boundary element method (BEM) can be reinterpreted with this theory. Moreoever, our approach offers guidance for discretizing complicated problems where straightforward discretizations may not be available.