1. Problem formulations

Formulating the problem is an essential step before applying the numerical method for solving it. It requires a good knowledge of electromagnetism and, to a certain extent, in-depth mathematical knowledge of operator manipulation and properties. The mathematical equations describing a physical phenomenon can either be solved directly, or manipulated to eliminate certain unknown quantities. In both cases, the equation(s) must usually be solved numerically. It's important to stress that the formulation dictates the advantages, disadvantages and limitations of the numerical procedure that will then be applied.

We'll also see that the choice of one or more unknowns dictates the type of spatial sampling used in the formulation. For example, the integral equation will be formulated in terms of sources (real or fictitious currents or associated loads). Consequently, the...