Mathematical Formulations for Electromagnetic Fields

There are various mathematical formulations for representing electromagnetic fields. They are equivalent to each other mathematically, but distinct in terms of numerical behavior. In this chapter, we will give a brief introduction to the three kinds of mathematical formulations employed in computational electromagnetics: vector partial differential equations, vector wave equations, and vector integral equations, which are the mathematical foundations of the finite-difference time-domain (FDTD) method, the finite-element method (FEM), and the method of moment (MoM), respectively.