The Study Of Edge Finite Element Method And Its Application In The Computation Of Engineering Eddy Current Problems

Combining with the concrete industrial task, the basic theory of edge finite element method and its application in 3-D nonlinear eddy current field and loss are deeply researched in this paper.By considering the situation that the use of both Whintey type and Mur type of edge element is widespread, various forms of vectorial interpolating function for these types are summarized. The relation between edge and nodal shape function is studied in this paper. It is proposed that although various forms of edge shape functions for Whintey type and Mur type of edge element are different for each other, the deriving principles of them are identical. The unified deriving method of them is given. The problem of uniqueness in 3D electromagnetic field computation using magnetic vector potential A as the variable is studied in this paper. The gauge problem using edge element for computing electromagnetic field is discussed mainly to perfect the formula in computing the tree of gauged edges.Considering the argument against the edge elements in the field of computing electromagnetic, a finite element software with A as variables is developed, which is interpolated by nodal elements, Whitney type and Mur type edge elements respectively. The Engineering-Oriented loss model(TEAM 21 Problem) and its extension version model 21.0 are computed, the computational accuracy, memory requirement and the convergence characteristic of PICCG method for them are compared, the advantage and disadvantage of both nodal and edge elements are discussed. It is shown that edge element and nodal element in computing engineering loss problem have strong and weak points respectively, we can't affirm or deny them entirely.Through theoretical analysis, the similarity of CG method for solving linear equations and variational method based on functional analysis is proposed, furthermore, the conclusion that the methods of BICG and CG are consistent when solving plural and symmetry equations is obtained in this paper. Based on above theoretical analysis, different kinds of PCG methods proposed in references at present are compared, and through numerical computation, the optimal PCG methods for solving finite element equations discreted by nodal elements and edge elements respectively is given in the computation of time harmonic eddy current field.A new method for computing 3D linear eddy current problems is developed. This method use H as the state variable in the whole regions of the problems. Because of particular treatments, the asymmetry of the coefficient matrix caused by the integral on the surface is avoided. It is used to compute the problem of TEAM WORKSHOP 21.0 and the result is analyzed. The edge-nodal coupled method for computing 3D eddy current problems is presented in this paper. The Galerkin FEM equations are deduced in detail. And the property of convergence are discussed. The PICCG method is improved in which the merits of PICCG and ICCG() method are combined. The three dimensional nonlinear eddy current field and the loss of the tie plate is analyzed in a three-phase, load-ratio voltage transformer, SFSZL7-31500/110, produced by the Baoding Tianwei Group Company Limited using the presentedmethod. The calculated leakage magnetic flux densities are compared with the measured values, and the results are satisfied for engineering design. The practicality of the method and the programs is further verified.At last, the problems that need to be further researched are pointed out.