The Natural Element Method Applied to Solve an Electrical Machine Problem

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Application of Mixed Finite Element and Natural Element Method in anti-periodic electromagnetic devices1

International audienceIn this paper, the Mixed Finite Element and Natural Element (Mixed FEM-NEM) Method is applied to determine the flux distribution in magnetic devices using its reduced magnetic circuit models. In this solution, the NEM is applied exclusively in the gap of the devices where deformations of the mesh are expected in case of movement and the FEM is applied in the remainder magnetic circuit. In order to reduce the computational cost, the use of anti-periodic boundary conditions is proposed allowing the reduction of the entire domain model. To show the effectiveness of the proposed methodology, the problem is solved by using FEM and NEM in separate, and by the mixed FEM-NEM. The obtained results are compared using an error estimator and the computational cost

Comparison of Natural and Finite Element Interpolation Functions Behavior at Interface between Different Mediums

International audienceThe 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

Comparison of natural and finite element interpolation functions behavior

International audienceIn this paper, the interpolation functions behavior of the natural element method (NEM) and the finite element method (FEM) are compared. It is discussed how the unknown in both methods affects the stiffness matrix and contributes to NEM better accuracy. The visibility criterion and the constrained NEM are also addressed, and a pseudoalgorithm is proposed to implement the constrained Voronoï diagram, which is the base for the constrained NEM. A complex heterogeneous magnetic problem is solved by both FEM and NEM methods and their solutions are compared. It is shown that for the same discretization, the number of contributions for NEM is in general bigger than those related to the FEM and better accuracy results for NEM

Comparison of Natural and Finite Element Interpolation Functions Behavior at Interface between Different Mediums

International audienceThe 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

Treatment of material discontinuities in natural element method for electromagnetic problems

International audienceIn this paper the treatment of material discontinuities in the Natural Element Method (NEM) are discussed. A visibility criterion and constrained Voronoi diagram are introduced in order to take account this difficult. The extension of NEM, the so-called C-NEM, is applied to solve electromagnetic problems. An electromagnetic problem is proposed and the approach is evaluated and compared with the traditional Finite Element Method (FEM)

Electromagnetic scattering analysis of arbitrary structures by the natural element method coupled with absorbing boundary condition

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Electromagnetic Scattering Analysis of Arbitrary Structures by NEM-ABC

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The Constrained Natural Element Method Applied in Electromagnetic Heterogeneous Models

In this paper the treatment of material discontinuities in the Natural Element Method (NEM) are discussed. A visibility criterion and the constrained Voronoϊ diagram are presented in order to take account this difficulty. The extension of NEM, the Constrained NEM (C-NEM), is applied to solve electromagnetic problems. An electrostatic problem is proposed and the approach is evaluated and compared with the traditional Finite Element Method (FEM)