Mixed finite elements for electromagnetic analysis

Jog, C. S.; Nandy, Arup

doi:10.1016/j.camwa.2014.08.006

Cited by 23 publications

(7 citation statements)

References 22 publications

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“…Mesh details are shown in Table 16 including the total number of equations. Table 17 shows the numerical values along with the computed zeros and they are compared with analytical results reported in [14], [17], [19]. The results of the edge elements (T8/Q12) demonstrate close matching with the analytical results.…”

Section: Cracked Circular Domain With Perfectly Conducting Surfacesmentioning

confidence: 61%

“…15. Mesh details of these elements are shown in Table 14 and 2 0 values are listed in Table 15 and are compared with analytical results reported in [14], [17], [19]. The results of the generated edge elements indicate a strong fit with the analytical results along with the correct multiplicity of eigen values.…”

Section: Circular Domain With Perfectly Conducting Surfacesmentioning

confidence: 84%

“…In order to capture singular eigen value in case of sharp edges and corners, in the regularization method we have to use a penalty parameter varying from 0 at the sharp edge to 1 at a large distance from the sharp edge.Also, in order to take care of inherent tangential continuity and normal discontinuity across material interface, potential formulation is used in nodal finite element framework [24], [4], [26], [1], [25]. In [19], a two field variation formulation in electromagnetics which can predict the eigen frequencies very accurately with correct multiplicities. There is no ad-hoc term in the mixed formulation as in the penalty function or the regularization method.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Conversion Technique from Nodal to Edge Finite Element Data Structure for Electromagnetic Analysis

Kamireddy,

Nandy

2021

Preprint

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Standard nodal finite elements in electromagnetic analysis have well-known limitation of occurrence of spurious solution. In order to circumvent the problem, a penalty function method or a regularization method is used with potential formulation. These methods solve the problem partially by pushing the spurious mode to the higher end of the spectrum. But it fails to capture singular eigen values in case of the problem domains with sharp edges and corners. To circumvent this limitation, edge elements have been developed for electromagnetic analysis where degree of freedoms are along the edges. But most of the preprocessors develop complex meshes in nodal framework. In this work, we have developed a novel technique to convert nodal data structure to edge data structure for electromagnetic analysis. We have explained the conversion algorithm in details, mentioning associated complexities with relevant examples. The performance of the developed algorithm has been demonstrated extensively with several examples.

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Section: Cracked Circular Domain With Perfectly Conducting Surfacesmentioning

confidence: 61%

Section: Circular Domain With Perfectly Conducting Surfacesmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

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A Novel Conversion Technique from Nodal to Edge Finite Element Data Structure for Electromagnetic Analysis

Kamireddy,

Nandy

2021

Preprint

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“…The key notion is the choice and evaluation of stress interpolation functions which is inspired from the work of Jog [29,30] in context of conventional FEA framework. The efficient FE implementation of the stated approach for large-deformation contact mechanics [2], structural acoustics [32], electromagnetic analysis [31], analysis of electromechanical systems [1], and coupled fluid-structure problem [38] confirms the effectiveness and robustness of the method. In the present study, the systematic evaluation of stress interpolation functions specific to the NURBS interpolations and its effective implementation in a two-dimensional linear elasticity regime is investigated.…”

Section: Introductionmentioning

confidence: 87%

A novel hybrid isogeometric element based on two-field Hellinger-Reissner principle to alleviate different types of locking

Bombarde¹,

Gautam²,

Nandy³

2021

Preprint

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In the present work, a novel class of hybrid elements is proposed to alleviate the locking anomaly in non-uniform rational B-spline (NURBS)-based isogeometric analysis (IGA) using a two-field Hellinger-Reissner variational principle. The proposed hybrid elements are derived by adopting the independent interpolation schemes for displacement and stress field. The key highlight of the present study is the choice and evaluation of higher-order terms for the stress interpolation function to provide a locking-free solution. Furthermore, the present study demonstrates the efficacy of the proposed elements with the treatment of several two-dimensional linear-elastic benchmark problems alongside the conventional single-field IGA, Lagrangian-based finite element analysis (FEA), and hybrid FEA formulation. It is shown that the proposed class of hybrid elements performs effectively for analyzing the nearly incompressible problem domains that are severely affected by volumetric locking along with the thin plate and shell problems where the shear and membrane locking is dominant. A better coarse mesh accuracy of the proposed method in comparison with the conventional formulation is demonstrated through various numerical examples. Moreover, the formulation is not restricted to the locking-dominated problem domains but can also be implemented to solve the problems of general form without any special treatment. Thus, the proposed method is robust, most efficient, and highly effective against different types of locking.

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“…Introducing a penalty term similar to the formulation in [26,27] and carrying out a suitable integration by parts, the variational statement corresponding to Eq. (10d) can be written as Z…”

Section: Variational Formulationmentioning

confidence: 99%

A monolithic finite-element formulation for magnetohydrodynamics

Nandy

Jog

2018

Sādhanā

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This work develops a new monolithic strategy for magnetohydrodynamics based on a continuous velocity-pressure formulation. The magnetic field is interpolated in the same way as the velocity field, and the entire formulation is within a nodal finite-element framework. The velocity and pressure interpolations are chosen so that they satisfy the Babuska-Brezzi (BB) conditions. In most of the existing formulations, a stabilized formulation is used that requires a stabilization term, and some associated mesh-dependent parameters that need to be adjusted. In contrast, no such parameters need to be adjusted in the current formulation, making it more user-friendly and robust. Both transient and steady-state formulations are developed for two-and threedimensional geometries. An exact linearization of the monolithic strategy ensures that rapid (quadratic) convergence is achieved within each time (or load) step, while the stable nature of the interpolations used ensures that no instabilities arise in the solution. An existing analytical solution is corrected. The coarse mesh accuracy is shown to be better compared with other existing strategies in several benchmark problems, showing that the developed formulation is both robust and efficient.

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Mixed finite elements for electromagnetic analysis

Cited by 23 publications

References 22 publications

A Novel Conversion Technique from Nodal to Edge Finite Element Data Structure for Electromagnetic Analysis

A Novel Conversion Technique from Nodal to Edge Finite Element Data Structure for Electromagnetic Analysis

A novel hybrid isogeometric element based on two-field Hellinger-Reissner principle to alleviate different types of locking

A monolithic finite-element formulation for magnetohydrodynamics

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