The Study On Space-Time Finite Element Method In Transient Electromagnetic Field

In this paper, the space-time finite element theory and its application technologies are studied and discussed. Furthermore the space-time finite element method is used to analyze the transient characteristics of electromagnetism equipments. The work is important to develop the numerical method for the transient electromagnetic field. The detailed work is as follow.In the basis theory of finite element method used in the transient engineering problem, the functional theory and the finite element theory are applied to studied the existence condition of a generalized variation principle, which is the basis of the space-time finite element method. Mathematically, many engineering problems are described by the differential equation, which includes the transient electromagnetic problem. The general correlation theories are presented to discuss the existence condition of a variation principle, which is named as the athwart problem of a variation principle. Furthermore the existence condition and the variation principle of the differential equation are discussed, and the theory gist of the step-time technologies is presented.In the basic theory, the basic STFEM theory is perfected, the variation principle in form of a convolution included is given and proved. Aimed to the differential equation in form of convolution and the functional presented by M. E. Gurtin, the matrix operator which includes the differential equation and the boundary condition is proved self-adjoint, furthermore a general variational principles in form of convolution and the preparation theorem are given and proved. In order to prove the theorems above, the Green formula in form of convolution is given. The content is important theory basic and the application condition of the STFEM.For the introduction of the STFEM in the transient electromagnetic field, a general functional in form of convolution is given, the STFEM formula and corresponding discretization formula are derived following the usual finite element variational procedure. For the transient electromagnetic field, the functional in form of convolution in which the vector variable A and boundaries are considered is given, the space-time finite element is analyzed and the STFEM formula are given.In the application research of the STFEM, the engineering practicability problems, which mainly are the medium nonlinear problem, the medium motion problem and the coupling problem between the magnetic field and the circuits, are thoroughly discussed. Aimed to the electromagnetic domain, the STFEM formulation in which the medium nonlinear is counted is given, the measure which deal with the medium motion is pointed, and the STFEM formulation in which the electromagnetic field and the circuits are coupled is given. The content is the application basis of the STFEM.In the practice of the space-time finite element method, the software based on the STFEM is built. The validity and practicability of the software are verified by calculating and analyzing the magnetic field on the great transformer and TEAM problem in which the experiment data are measured. Furthermore the software is used to analyzing the transient characteristics of the great transformer, the permanent magnet synchronous motor and the AC excited generator.