“Regular element” global SLAE of the finite element method when simulating electromagnetic processes of electric devices

Abstract

The article is devoted to mathematical and simulation modeling of electromagnetic processes of electric devices (ED). The development of industry, transport, power facilities, agriculture, and household services, health care leads to creation of electrical devices and systems for various functional purposes. It complicates the design (geometry) of electromagnetic and magnetic systems, improves magnetic and electrical characteristics of ED materials. The development of new software and hardware allows solving mixed (connected) tasks of simulating various physical processes in ED, electrical and electromechanical systems. However, general-purpose software complicates its engineering assimilation and implementation into production. The stage of ED numerical simulation modeling based on the finite element method when their investigating and designing is offered to be reduced and cheapened by changing the process of developing a global system of linear algebraic equations (SLAE) out of the system of elemental equations. The purpose of the work is to develop an algorithm to form global SLAE based on recurrent relations for its coefficients. The study subject is quasi-variable and magneto static vector models of ED electromagnetic processes, electro technical and electromechanical systems. Tasks are: developing of a “regular element”, obtaining recurrent relations for global SLAE coefficients. Research methods are: numerical calculations based on the Galerkin’s projection-grid method along with the finite element method (FEM). Results are: a seven-point “regular element” for a regular triangulation network from triangular finite elements (FE) of arbitrary shape and rectangular triangles has been developed; recurrent relations for global SLAE coefficients have been determined; a possibility of obtaining engineering techniques for investigating ED with minimal computer’s dynamic memory expenses has been shown on the example of calculating a linear induction motor (LIM).