Algebraic Topological Method: An Alternative Modelling Tool for Electromagnetics

Abstract

We begin with a simple question: what is the real need for field vectors and differential equations while modelling electromagnetic problems? Particularly, when all what we can practically measure in electromagnetics are only scalars, the traditional approach to modelling in electro-magnetics is proving to be more mathematical than physical. In addition, the use of differential equations takes us through an indirect path for modelling underlying physics. We cannot directly translate continuous differential equations into numerical algorithms because computers need discrete formulations. In this work, we discuss a direct discrete and computationally competitive tool using only physically measurable scalar quantities called the algebraic topological method for modelling different electromagnetic problems. We will also highlight areas of current and future research in this domain.