Research On New Approach Of Radial Basis Function Meshless Method For Numerical Electromagnetic Computation

With continuous development for more than four decades, finite element method (FEM) has become an efficient and powerful technique for the numerical computation of electromagnetic filed. On the other hand, there are still some open problems because the accuracy of FEM highly depends on the meshing methods. Therefore, meshless method has been a topic of much interest recently as only a set of nodes instead of meshing nodes are required in the method. The radial basis function (RBF) collocation meshless method does not require background grid and is easy to implement, it is a very promising numerical method in the field of numerical computation of electromagnetic filed. However, this method has some problems as well through further research work. RBF is theoretically a high-order derivative smooth function. It is hard to maintain a good fitting accuracy when RBF model is used to fit the cusp catastrophe functions, and the fitting results are difficult to converge. Therefore, a popular approach to solve the abovementioned problem is to combine RBF collocation method with the domain decomposition method, the latter can deal with the cusp catastrophe points as interfaces between different subdomains and fit them respectively. Because of this change, the combined method is complicated to implement. Through analyzing the advantages and disadvantages of the classic FEM and RBF collocation method, this thesis presents a new hybrid approach for RBF meshless method for the numerical computation of electromagnetic filed. By taking full use of the convenience of the FEM in dealing with the boundary conditions, the new approach can overcome the difficulties of domain decomposition in traditional RBF collocation method. A variety of computational electromagnetic problems have been analyzed and calculated by the new method. The main work of this thesis includes the following aspects.Firstly, based on a survey of RBF collocation method, we introduce current research achievements of our group on this method. Moreover, by analyzing the problems of a domain-decomposition RBF collocation method proposed in our previous work, a revised method is proposed to improve the stability and accuracy of the new method, followed by the verification of several numerical examples.Secondly, we present a new radial basis meshless method by combining with the FEM. The new method can be taken as a new kind of domain decomposition RBF collocation method. It treats the subdomains as the meshes in the FEM, which gets the numerical results in the sub-region by using RBF collocation method and deals with the entire computation domain by FEM. This hybrid approach inherits the advantages of both methods and overcome their shortcomings. Then, detail steps of the method are described, and numerical examples demonstrate the effectiveness of the new method. The calculation results agree well with the analytical solution, and also have been compared with the FEM results.Thirdly, the new RBF collocation method is proposed to solve multi-media moving conductor eddy current problems. According to the definition of magnetizing current of permeability, based on the superposition principle, the field of magnetizing current can be computed separately. With this new field decomposition strategy, we can perfectly overcome the difficulty of the sub-regions and nodes refreshed by time steps for multi-media moving conductor eddy current problems. The effectiveness of the method is verified through the investigation of the TEAM workshop problem28. Furthermore, the new field decomposition strategy can be applied to the FEM.Finally, the method has uniformly distributed nodes and regular rectangular subdomains in general situations. However, flexible nodes set and different shapes of sub-regions are often encouraged in real problems. In order to extend the range of this method, we introduce two kinds of different nodes set, and analyze the results of triangle sub-region. Meanwhile, new method is proposed to improve the fitting accuracy for the problems with jump discontinuity boundary conditions. The new method uses FEM to calculate the subdomains with jump discontinuity boundary condition and new RBF collocation method for other subdomains.