Comparison of Natural and Finite Element Interpolation Functions Behavior at Interface between Different Mediums
Résumé
The natural element method (NEM) is a meshless method based on theVoronoï diagram and the natural neighbor concept. Unlike the finite elementmethod (FEM) whose interpolation functions are supported only by theelement nodes, the NEM interpolation functions are supported by all neighborsnodes from the influence domain. In Figure 1(a) note that the node highlighted(red node) on interface is influenced by seven neighbour nodes (yellownodes). As the number of nodes in the influence domain are in general biggerthan that presented on the elements, the interpolations for NEM results inbetter results that those obtained for FEM one. This feature leads to a betterNEM interpolation of quantities especially in the interface between differentmediums.For the purpose of analysis, a 2D electric vector potential problem consistingof a conductor strip of copper and aluminium shown by Figure 1(a) isaddressed in this paper. The Sibson shape functions are used for NEMinterpolation while first order triangular element are used for FEM one. Bothmethods use a 125 nodes discretization. Figure 1(b) shows the currentdistribution on the interface between copper and aluminum. The result isvalidated by comparison with a very refined FEM mesh. The NEM and FEMerrors are evaluated for the abovementioned discretization been the FEM oneapproximately 2.3 higher than that of NEM one. This verifies the NEMaccuracy to interpolate physical quantities in interfaces.