Comparison Between NEM and FEM in 2-D Magnetostatics Using an Error Estimator

Abstract

This communication deals with a comparison between two methods of discretization: the well known finite element method and the natural element method that is a meshless method. An error estimator, based on the nonverification of the constitutive law, is used. This estimation has been applied to two examples: a device with permanent magnets and a variable reluctance machine.

Electromagnetic Scattering Analysis of Arbitrary Structures by the Natural Element Method Coupled With Absorbing Boundary Condition

“…Numerical procedures for evaluation of (5) and computational costs analysis of NEM is given by [8] and [9]. Fig.…”

“…For example, nodes situated on both sides of a crack would be seen as natural neighbors, and thus would have an undesirable mutual influence. To overcome this problem, some authors have proposed to introduce a constrained Delaunay triangulation associated with a criterion of visibility to avoid nodes that are near in distance but located on both sides of a border to become natural neighbors (so-called (C-NEM) in [6] and [9]). …”

“…The main interest of NEM lies in its interpolation property, which allows enforcing essential boundary conditions in an easy way as with the FEM [8]. In addition, this method retains the natural capacity of treating heterogeneous domains and presents similar numerical behavior with a better convergence compared to FEM in some cases [9]. Manuscript The aim of this paper is to investigate the feasibility and the accuracy of the NEM when applied to study electromagnetic scattering problems.…”

A mixed finite element/meshless natural element method for simulating rotative electromagnetic machines

“…For comparison purposes we use the error estimator introduced in [3] in the natural element method framework, which is based on the solution of both complementary potential formulations. It will be applied to quantify the accuracy of the different solutions as well as to compare C-NEM and FEM solutions.…”

“…This error estimator was introduced in [26] and is often used to estimate numerical errors in static electromagnetism. This estimator was recently used to compare finite element and meshless natural element solutions in the case of magnetostatics (without taking into account movement) in [3]. In the present work we are applying this estimator in order to compare both methods when the movement is also taken into account.…”