Three-Dimensional Element 'Hyper-Cube' and Algorithm for Forming the Coefficients of the Global SLAE of the Finite Element Method at Calculations of Magnetic Fields of Electrical Engineering Devices

摘要

The article is devoted to calculation of three-dimensional magnetostatic fields of electrical engineering devices of fixed or with linear motion trajectory of various functional purposes by the finite element method using a regular finite element network. The aim of the research is to create an algorithm for forming coefficients of global SLAE of the finite element method on the basis of three-dimensional finite element 'hyper-cube' when solving magnetostatic problems for obtaining engineering methods. The study subject is magnetostatic three-dimensional vector models of electromagnetic processes of electrical engineering devices, electrical engineering and electromechanical systems and methods of their calculation. The tasks are: to develop three-dimensional elements such as 'cube' and 'hyper-cube', to obtain recurrent relations for global system of linear algebraic equations (SLAE) coefficients. Research methods are: numerical calculations based on projection-grid method of the Galerkin in combination with the finite element method. The results are: a three-dimensional element of 'cube' and 'hyper-cub' type for a three-dimensional regular network of the finite element method has been offered, and recurrence relations for global SLAE coefficients are developed when working out engineering methods for calculating magnetostatic fields and their power characteristics in electrical engineering devices with minimal costs of the computer dynamic memory.