Three-dimensional electromagnetic wave analysis using high order edge elements

Ahagon, Akira; Kashimoto, T.

doi:10.1109/20.376375

Cited by 24 publications

(14 citation statements)

References 11 publications

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“…The convergence behavior is shown in Fig. 3, where the curves and correspond, respectively, to the elements given in [5], [8]- [10] and our proposed one [14]. It can be seen that our element has a good convergence behavior as Lee's.…”

Section: Comparison Of Some 2nd Order 1-form Elementsmentioning

confidence: 82%

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High order differential form-based elements for the computation of electromagnetic field

Ren

Ida

2000

IEEE Trans. Magn.

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Section: Comparison Of Some 2nd Order 1-form Elementsmentioning

confidence: 82%

“…per facet. Different types of elements have been developed [5], [8]- [10]. We have applied them in a formulation in terms of magnetic vector potential to solve magnetostatic problems [13] and in a combined magnetic vector potential and electric scalar potential formulation to compute eddy currents [14].…”

Section: Comparison Of Some 2nd Order 1-form Elementsmentioning

confidence: 99%

High order differential form-based elements for the computation of electromagnetic field

Ren

Ida

2000

IEEE Trans. Magn.

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“…The difference is small in the case of big ratios. Because in this case, the curl-curl term dominates and the curl of Lee's basis satisfies the dependence relation (6). However, when the frequency increases (the ratio diminishes), it is the term of the edge element function itself that becomes dominant.…”

Section: Comparison Of Resultsmentioning

confidence: 99%

“…To check this point, let us see the dependence of those three functions. Using again the rotation operator , we note that Ahagon's and Youlsis' elements satisfy the relation: (6) This means that taking any two of three functions spans the same space, and hence we can expect that the choice of any two of three functions will not influence the numerical results. Instead, Lee's element does not fulfill this relation, but .…”

Section: B On the Asymmetry Of Facet Related Basis Functionsmentioning

confidence: 99%

Solving 3D eddy current problems using second order nodal and edge elements

Ren¹,

Ida

2000

IEEE Trans. Magn.

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Abstract-Several 2nd order nodal and edge elements have been applied in a potential formulation to solve 3D eddy current problems. The asymmetry of the facet related functions in the edge element basis is discussed. A new basis is proposed. Application of a gauge condition for the uniqueness of vector potential is cumbersome in the case of high order elements. This work shows that the system converges without explicit gauge condition when using the bi-conjugate gradient method. The performance of different elements is compared through an example.Index Terms-Eddy currents, finite element modeling, second order edge elements.

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“…Due to the limited space available, let us just report some recent results of the present authors which widen significantly the class of a priori reliable finite elements. It is proved in [7] that the elements proposed by Kameari [2], Ahagon and Kashimoto [8], Yioultsis and Tsiboukis [9], Peterson et al [10,3] and Lee et al [1] are spurious-free.…”

Section: High-order Spurious-free Finite Element Approximationsmentioning

confidence: 99%

Reliability and Performances of Finite Element CAD Tools for the Solution of Microwave Problems

Fernandes

Raffetto

2001

31st European Microwave Conference, 2001

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The target of this paper is two-fold. On the one hand, we address the question of the reliability of' many recently proposed high-order finite elements. On the other hand, new quadrilateral edge elements are proposed and the improvements of the performances they permit are stressed. INTRODUCTIONHigh-order edge elements make it possible to improve the performances of finite element simulators. For this reason, in recent years, quite a lot of high-order edge elements have been introduced [1,2,3] after the pioneering work of Nedelec [4]. However, before analysing their performances, one should establish the reliability of the finite elements considered. This is an important issue since, for many years, finite element simulators were plagued by the so-called spurious modes. Thus, in this paper, we firstly report some recent results of the present authors assessing the reliability of many of the new elements recently introduced. Once the class of a priori reliable finite elements has sufficiently been widened, it makes sense to compare the performances in order to find the best one. However, the "best" element could also be an element not defined so far and, for this reason, it is important to keep on looking for new and more efficient elements. As a first attempt in this direction, we will firstly define a new element on rectangles and then we will compare its performances with those of other well known spurious-free elements. In the simple example considered the performances of the new element are significantly better than those of all existing elements of the same order.

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Three-dimensional electromagnetic wave analysis using high order edge elements

Cited by 24 publications

References 11 publications

High order differential form-based elements for the computation of electromagnetic field

High order differential form-based elements for the computation of electromagnetic field

Solving 3D eddy current problems using second order nodal and edge elements

Reliability and Performances of Finite Element CAD Tools for the Solution of Microwave Problems

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