Learning Solutions for Electromagnetic Problems Using RBF Network-Based FE-LSSVM

Solutions to most electromagnetic problems use numerical methods, such as the finite element method (FEM), element free method (EFM), and soft computing method. To decrease the computational complexities of these methods, this paper presents an approach for solving electromagnetic problems, called radial basis function (RBF) network-based finite element least square support vector machine (FE-LSSVM). First, the expansion of approximate solutions by the proposed method uses the same structure as the RBF network method. Second, governing equations of electromagnetic problems are transformed to weak integral forms and variational formulations of FEM. Finally, Dirichlet boundary conditions are handled in the LS-SVM framework, which are considered as constraints of an optimization problem. By the Lagrange multiplier method, the quadratic programming problem can be transformed to a problem requiring the solution of a system of equations. The advantages of the proposed method are to directly satisfy the natural boundary conditions of the electromagnetic equations and remarkably improve the calculation accuracy. To verify the efficiency of the method, four categories of electromagnetic problems are investigated by using the proposed method. An analytical method and FEM are also carried out as comparisons to prove the advantages of the method proposed in this paper.