The Application Of EBE Finite Element Method In The Calculation Of Three-Dimensional Electromagnetic Field

With the development of UHV power grid,the physical size of large power equipment is getting bigger and bigger,considering the penetration depth,and huge amounts of meshes are needed to analyze the electromagnetic field in the equipment accurately using the finite element(FEM).So the computation scale will be too large to be calculated by conventional serial FEM.Therefore,the parallel algorithms has been researched by more and more researchers and applied to numerical computation.In this paper,the application of the element level parallel algorithm EBE(element-by-element)finite element method in the calculation of 3D electromagnetic field is researched,and the corresponding finite element calculation program is developed with the C++ language.In this paper,the EBE finite element method is derived in detail combined with the traditional finite element method,and the numerical calculation method related to the algorithm,the preconditioning technology of the coefficient matrix and the treatment of the boundary condition are researched.The 3D conjugate gradient method based on EBE finite element method and based on coefficient matrix Jacobi preconditioning are derived to solve EBE finite element equations.On the basis of the 2D EBE method,combined with the weighted residual method of3 D electromagnetic field analysis,the 3D EBE finite element mathematical model is established for tetrahedral element,and the discrete model and boundary treatment of the 3D EBE finite element are derived in the thesis.The corresponding 3D EBE-CG method and the3 D EBE-J-PCG method are developed in the C++ language.The accuracy and effectiveness of the method and program are verified by the magnetic field produced by the long direct current carrying wire.The C++ programs of 3D EBE-CG method and EBE-J-PCG method are applied to the main magnetic field calculation of a single phase transformer and a three-phase transformer.The main magnetic field distributions are obtained through the visualization processing of the calculation results.Through the analysis and comparison of calculation results,it is found that the convergence of EBE finite element method is obviously improved after preconditioning.