REVIEW OF ALTERNATIVE APPROACHES TO SIMULATION OF THE ELECTROMAGNETIC SITUATION AT A HIGH-VOLTAGE ELECTRIC SUBSTATION

Abstract

In the field of electromagnetism, boundary value problems are problems for which the electromagnetic field in a given region of space is determined from knowledge of the field over the boundary of the region. To solve boundary problems, traditional numerical methods are usually used, such as the finite difference method (FDM) in the time domain and the finite element method (FEM). However, these methods involve discretizing the domain to reduce it to a higher order system of linear algebraic equations and finding a solution for them. As you know, these methods are not local, i.e. they do not give the value of the solution directly at an arbitrary point where the field is to be defined, but its value must be extracted from the full solution of the field, and therefore cannot be processed in parallel. In this regard, the article considers the use of neural networks for boundary value problems with the Dirichlet boundary condition and with mixed boundary conditions.