THE MATHEMATICAL MODEL OF TWO-DIMENSIONAL ELECTROMAGNETHIC FIELD
H. S. Sukiasyan · Proceedings of National Polytechnic University of Armenia ELECTRICAL ENGINEERING ENERGETICS · 2024
The purpose of this work is to develop a mathematical model of two-dimensional electromagnetic field, i.e. to construct a system of axioms (assumptions) that we unconditionally accept, although they do not correspond to the real electromagnetic field, but approximate it quite well. A mathematical model of two-dimensional electromagnetic field is constructed based on four assumptions: 1. Boundedness: we assume that on an infinite plane there is a bounded convex domain, outside which the field is zero. 2. Existence of nodes: we assume that in the domain there is a finite set of points, called nodes. All calculations of potential values are carried out only at internal nodes․ 3. Existence of neighbors: we assume that all pairs of nodes are divided into two types: neighboring and non-neighboring, and only neighboring nodes interact. 4. Discretization: we assume that the magnetic permeability of the medium is discrete, i.e. is a piecewise constant function. It is shown that within our mathematical model, from Assumptions 1 – 4, it follows that the electromagnetic potential is necessarily a piecewise linear function. It is shown that within our mathematical model, minimization of the energy functional leads to a system of nonlinear equations, the number of equations is equal to the number of internal nodes. It is proved that within our mathematical model, from Assumptions 1 – 4, it follows that for the numerical solution of the resulting system of equations, the optimal mesh is the Delaunay triangulation. The results are illustrated by an example of numerical solution of a field problem for electromagnetic systems with magnetorheological fluid using the FEMM tool. It is shown that the FEMM application package corresponds to our model.