Computational Performances of Natural Element and Finite Element Methods

Maréchal, Yves; Ramdane, Brahim; Botelho, Diego Pereira

doi:10.1109/tmag.2013.2285259

Cited by 13 publications

(9 citation statements)

References 6 publications

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“…Contrary to the finiteelement analysis [13], [32] and also new methods (for example, the natural element method [33]), the magnetic charges approach considers the integration of (29) and (30) only with reference to the specific regions of interest. In this way, accuracy and time computations can be highly increased and reduced, respectively.…”

Section: Magnetostatic Field Evaluationmentioning

confidence: 99%

Symmetry of Magnetostatic Fields Generated by Toroidal Helicoidal Magnets

Muscia

2015

IEEE Trans. Magn.

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In this paper the axial symmetry of the magnetic field generated by a permanent magnet of helicoidal toroidal kind is shown. In the first part of the paper we illustrate the shape of the magnet and the number of areas where the field is calculated to demonstrate the symmetry. We define quantitatively the size of the toroidal helical magnet and the regions where the magnetostatic field is evaluated. The field is carried out for each angular sector that represents the regions where the magnetic flux density is computed. This calculation is performed with reference to a matrix of points belonging to each sector. Two sets of evaluations are performed. The first one is referred to a less dense matrix of points relative to all the regions. The aim of this computation is to demonstrate the axial symmetry of the field. The second set of calculations concerns the field evaluation by using a much higher dense matrix of points. By using this data we are able to interpolate the same field with a high precision. This second evaluation of the field is carried out with reference only to the flat region facing the first coil of the helical toroidal magnet. The use of an interpolation surface through the final points of the magnetic induction vectors previously computed allows a very fast evaluation of the field virtually in all the infinite points of the angular sector. The symmetry enables us to drastically reduce the time computation of the magnetostatic field in the points of interest

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Section: Magnetostatic Field Evaluationmentioning

confidence: 99%

Symmetry of Magnetostatic Fields Generated by Toroidal Helicoidal Magnets

Muscia

2015

IEEE Trans. Magn.

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“…In literature, several formulas are used to calculate this shape function . Among the most used are the Sibson functions, which may be determined in analogy with classical FEM shape functions as the ratio of surfaces in the case of triangles . The same principle is applied to Voronoï cells to achieve Sibson shape functions.…”

Section: The Natural Element Methodsmentioning

confidence: 99%

“…Many studies have shown that in general the NEM interpolation presents better results than the FEM interpolation . A comparison between the NEM and FEM interpolations behavior can be performed considering the contributions in the stiffness matrix to evaluate the accuracy of the NEM approach.…”

Section: The Nem and Fem Interpolation Behaviormentioning

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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“…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%

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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Computational Performances of Natural Element and Finite Element Methods

Cited by 13 publications

References 6 publications

Symmetry of Magnetostatic Fields Generated by Toroidal Helicoidal Magnets

Symmetry of Magnetostatic Fields Generated by Toroidal Helicoidal Magnets

Comparison of natural and finite element interpolation functions behavior

Higher Order NEM and FEM Accuracy Comparison

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