TRANSITION FROM A DIFFERENTIAL EQUATION TO FINITE SYSTEM OF EQUATIONS WITH A FINITE NUMBER OF UNKNOWNS USING THE EXAMPLE OF TWO-DIMENSIONAL ELECTROMAGNETIC FIELD

Abstract

The purpose of this work is to develop a mathematical model of a two-dimensional electromagnetic field, i.e. to construct a system of axioms (assumptions) that allow an adequate transition from a differential equation to a finite system of equations with a finite number of unknowns. It is shown that within the framework of our mathematical model, the electromagnetic potential is necessarily a piecewise linear function. It is proved that within the framework of our mathematical model, the optimal grid for the numerical solution of the resulting system of equations is the Delaunay triangulation. The results are illustrated by an example of a numerical solution of a field problem for electromagnetic systems with magnetorheological fluid using the FEMM environment tool. It is shown that the FEMM application package corresponds to our model.It is shown that within our mathematical model, from Assumptions 1 - 4 it follows that the electromagnetic potential is necessarily a piecewise linear function.