Abstract
An electromagnetic simulation often requires vector edge-based shape functions. In a finite-element method (FEM) context, vector shape functions are designed for keeping the tangential continuities and the normal discontinuities between elements, which correspond to the physical nature of electromagnetic fields. However, in the meshless methods context, the construction of vector shape functions is not direct and a very little work has been published on a vector interpolation. Presenting the typical characteristics of meshless methods, the natural element method (NEM) has proved to be able to provide more accurate and computationally efficient solutions than the standard FEM for node-based approximations. This paper is the first proposal of an NEM-based vector interpolation for polygonal/polyhedral cells. Results show that the implemented approach provides better accuracy than the edge-based FEM for a given number of degrees of freedom.
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