The Study On Element-Free Method And Its Application On Computational Electromagnetics

Element-free Galerkin (EFG) method is a novel effective method for solving electromagnetic computation, which is suitable for dealing with small air gap and membrane problems, which are difficult by finite element method (FEM), so it could make up the defection of FEM. The dissertation studied on the electromagnetic problems by EFG. The dissertation consists of four parts:Firstly, in order to increase the solving efficiency, the multigrid method was used in EFG, and a multigrid method of element-free Galerkin was presented in the paper. The multigrid iterative technique was extensively introduced to FEM frame, which could increase solving efficiency. In order to resolve low computational efficiency of element-free Galerkin method, the dissertation introduced the accelerated iterative multigrid method to the element-free Galerkin discrete field, proposed a multigrid method of element-free Galerkin (EFG-MG). The disposition on solutions of coarse grid nodes and fine grid nodes, in addition to the construction of coarse nodes and the restriction operator were different from the traditional MG. It was used for numerical computation of electromagnetic field problems, and the high efficiency of element-free Galerkin method was proved by examples. For the same element-free model, the CPU time of MG method is less than ICCG method for different freedom numbers. It indicates that the computational efficiency of MG is higher than ICCG.Secondly, the dissertation studied on the nodes distribution of EFG. The errors of the solutions are influenced greatly by the distribution of nodes of element-free method when using EFG. In order to reduce the errors of calculation, a new method on distribution of element-free nodes in irregular electromagnetic field domain was developed. In the method, firstly, the self-organizing feature map was used to generate background cells; secondly, the element-free nodes were determined by the evaluation points. The method is convenient for generating reasonable distribution of nodes with high solving accuracy. Thirdly, the dissertation studied on the numerical integration of EFG. The support domain of circular shape was used to construct integral domain, the Gauss numerical integration methods were used to overlapping area of the supporting domains. Based on the Gaussian integral formula, the curve equations rel ated with the positions of Gaussian integral points and weights to the node distance were derived. The method doesn't need background cell integration, is a pure element-free method. It is very convenient for numerical integration, by which the solving accuracy is increased.Finally, the dissertation presented a new coupling model for coupling element-free Galerkin method with finite element method (EFG-FEM). The coupling model was based on overlapping domain decomposition method (DDM), in which the domain was decomposed into FEM subdomain and EFG subdomain; then the FEM subdomain and EFG subdomain were solved in turn by iterative method, until the solutions of the domain were obtained. The solutions are more accurate than Belystchko's coupling method, and can eliminate influence of irregular interface shape.