Electromagnetic Problems Modeling Using Algebraic Topological Method

Abstract

We can solve electromagnetic problems using two main mathematical tools: vector calculus and differential equations. These tools command the computational electromagnetic domain. However, these tools are not always needed for the realistic modeling of electromagnetic problems. In reality, we are interested in the measurement of scalar quantities in electromagnetics, not vector quantities. Conventional electromagnetic simulation approaches are proving to be more mathematical than physical. Furthermore, the use of differential equations leads us along a different route for modeling fundamental physics. Since computers need discrete formulations, we can't directly transform continuous differential equations into numerical algorithms. The algebraic topological method is a direct discrete and computationally ambitious technique that uses only physically measurable scalar quantities. This paper simulates a parallel plate capacitor using global variables and calculating and comparing the potentials with the analytical method. The measured results show a good agreement between the analytical and the algebraic topological methods.