Natural Element Method Applied to Electromagnetic Problems

In this paper, the natural element method (NEM), which is part of the meshless methods family, is used to solve electromagnetic problems. It is an interesting alternative to the finite element method. This method is based on the Voronoï diagram and the natural neighbors. These two concepts and the construction of the shape function are presented. The NEM shape functions are interpolant and linear on the boundary of the studied domain. This property allows a natural coupling with the finite element method. A 2D electrostatic example is studied. Results are compared to those obtained by FE method in order to illustrate the interest and the relevance of the new method. A second example of an electric machine is proposed in order to illustrate the ability of the NEM to be naturally coupled with FEM.