Natural Element Method Applied to Electromagnetic Problems

Maréchal, Yves; Ramdane, Brahim

doi:10.1109/tmag.2013.2242875

Cited by 7 publications

(10 citation statements)

References 7 publications

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“…Furthermore, the shape functions degenerate to a simple linear interpolation at the borders, allowing direct coupling with FEM [5]. Nevertheless, the produced interpolation presents only linear completeness [4].…”

Section: Natural Element Methodsmentioning

confidence: 99%

“…The treatment of interfaces between materials was made by combining the concepts of C-NEM [5] and node repeating. It means that, on interfaces, the Voronoï cells were truncated and the nodes were not eliminated in the implementation of (4).…”

Section: B Boundary and Interface Conditionsmentioning

confidence: 99%

“…Accuracy and computational efficiency of the standard NEM scheme was compared with the FEM first-and second-order approximations in [5] and [6]. In this paper, a higher order NEM is obtained by means of the de Boor algorithm [7], [8] and its accuracy is compared with the FEM.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Higher Order NEM and FEM Accuracy Comparison

Botelho

Maréchal²,

Ramdane³

2015

IEEE Trans. Magn.

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The natural-element method (NEM) has proved to be able to provide more accurate and computationally efficient solutions than the finite-element method (FEM) for first-order consistency approximations. However, higher order approximations in the NEM framework are not obtained straightforwardly. This paper addresses a method of constructing higher order approximations out of the standard first-order NEM shape functions. This process is achieved through the de Boor algorithm. Accuracy of the scheme is compared with FEM. Results show that in second-order approximations context the NEM is still able to provide better accuracies for a given number of degrees of freedom.Index Terms-De Boor, finite-element method (FEM), natural-element method (NEM), second-order consistency, splines.

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Section: Natural Element Methodsmentioning

confidence: 99%

Section: B Boundary and Interface Conditionsmentioning

confidence: 99%

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Higher Order NEM and FEM Accuracy Comparison

Botelho

Maréchal²,

Ramdane³

2015

IEEE Trans. Magn.

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“…The NEM approach is based on the Voronoï diagram and the natural neighbors concept. The convergence of the NEM has been previously studied for different applications . And the NEM main interest lies in its interpolation property, which allows enforcing essential boundary conditions and interface conditions in an easy way as with the FEM …”

Section: Introductionmentioning

confidence: 99%

Comparison of natural and finite element interpolation functions behavior

Gonçalves

Afonso

Coppoli

et al. 2017

Int J Numerical Modelling

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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

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“…A VAILABILITY of powerful numerical tools to analyze field problems by means of both conformal mapping via inversion of the Schwarz-Christoffel (SC) formula [1]- [3] and finite element methods (FEMs) [4]- [6] suggests to discuss an old problem from a methodological point of view, and to make useful comparisons, considering the recent meshless methods too [7]. The standard SC formula allows us to perform very accurate calculation on domains limited by polygonal boundaries, but this can introduce singularity artifacts, whereas a curved boundary would be more appropriate.…”

Section: Introductionmentioning

confidence: 99%

A Simple Procedure to Optimize Small Radius Rounded Corners Obtained From Schwarz–Christoffel Conformal Transformations

Costamagna

2015

IEEE Trans. Magn.

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Both conformal mapping via Schwarz-Christoffel (SC) formulas and finite element methods (FEM) can provide accurate results in analyzing 2-D electric or magnetic fields. In the presence of curved boundaries with small radius of curvature, the first are normally constrained to introduce piecewise straight lines. The original contribution of this paper consists of presenting a reliable but simple procedure to smooth several sharp vertices of a polygonal boundary by the formula for rounded corners, and comparing the results with those obtained by replacing sharp corners with piecewise straight lines. Differences are perceived only in close proximity, and this quantitatively explains the similar results obtained from maps and from FEMs and provides reliable assessment of the obtainable results. Two approaches are followed. According to the first, sharp corner geometries are directly mapped into rounded corner ones, accepting small changes in the whole structure, and negligible only for small corner radii. According to the second, the simple optimization procedure of the SC prevertices allow us to match the original geometry in all details.Index Terms-Conformal mapping, finite elements, inverse problems, Schwarz-Christoffel (SC), static fields.

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Natural Element Method Applied to Electromagnetic Problems

Cited by 7 publications

References 7 publications

Higher Order NEM and FEM Accuracy Comparison

Higher Order NEM and FEM Accuracy Comparison

Comparison of natural and finite element interpolation functions behavior

A Simple Procedure to Optimize Small Radius Rounded Corners Obtained From Schwarz–Christoffel Conformal Transformations

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