Element Differential Method for Solving Linear and Nonlinear Electromagnetic Problems

Abstract

A novel numerical method named element differential method (EDM) is first presented to solve linear and nonlinear static electromagnetic problems. The main idea of this method is to use the direct differentiation formulation of the shape functions of Lagrange isoparametric elements to evaluate geometry and physical variables. A new collocation method is proposed to establish the system of equations, in which the governing equation is collocated at the internal nodes of the elements, the continuity conditions of tangential component of magnetic field intensity and normal component of electric displacement vector are collocated at interface nodes between elements, and Neumann boundary conditions are collocated at outer surface nodes. Compared with the finite element method, there is no need to use any variational or energy principles to establish the system of equations and there is no requirement for integral evaluation. The derived spatial derivatives can be directly substituted into the static electromagnetic governing equations and the boundary conditions to form the final system of algebraic equations. Three 2D numerical examples are used to verify the correctness and effectiveness of the presented method for solving linear and nonlinear static electromagnetic problems.