A sparse matrix open boundary method for finite element analysis

Lowther, D.A.; Freeman, E.M.; Forghani, B.

doi:10.1109/20.34292

Cited by 60 publications

(19 citation statements)

References 7 publications

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“…In finite element modelling the term "transformation technique" refers to the idea that a BVP can be represented with multiple coordinate systems and particularly open-boundary problems have been solved this way [3], [4].…”

Section: Equivalent Representations Of Bvpmentioning

confidence: 99%

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Parametric Models in Quasi-Static Electromagnetics

2009

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Section: Equivalent Representations Of Bvpmentioning

confidence: 99%

“…3 The movement of the magnet changes the geometry only in a small part of the problem domains. To restrict the effects of the movement to the near neighborhood of the magnet, we enclose the magnet by four triangles and four quadrilaterals as shown in Fig.…”

Section: Numerical Example: Linear Motionmentioning

confidence: 99%

Parametric Models in Quasi-Static Electromagnetics

2009

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“…Em muitas aplicações do eletromagnetismo, a região externaé modelada com o objetivo de aumentar a precisão numérica do cálculo das variáveis eletromagnéticas na própria região interna, ocupada pelo dispositivo em estudo. Já para um outro grupo de aplicações, que incluem os estudos de blindagem e interferência eletromagnética, a estimativa precisa das variáveis eletromagnéticas em posições distantes do dispositivoé mais importante que a avaliação da distribuição dessas variáveis na região ocupada pelo dispositivo [9]. O modelo numérico simplificado, proposto inicialmente para o cabo coaxial energizado, possui fronteiras que coincidem com os limites geométricos do dispositivo e, por isso,é caracterizado como um problema interior.…”

Section: Modelo Numérico Com Fronteira Exteriorunclassified

Análise de cabos coaxiais cilíndricos usando a técnica dos elementos finitos

Nogueira

2007

Rev. Bras. Ensino Fís.

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A nova geração de simuladores de campos eletromagnéticos pode ser usada no ensino de eletromagnetismo sem que o usuário conheça com profundidade a metodologia usada no desenvolvimento desses programas computacionais. A teoria da linha coaxial cilíndricaé usada para ilustrar a aplicação desses programas como ferramenta de ensino. A solução analítica do problemaé usada para avaliar a precisão numérica dos resultados obtidos utilizando diferentes subdivisões das malhas de elementos finitos. A relação entre minimalidade energética e distribuição de potenciais elétricosé usada para explicar como diferentes discretizações do modelo afetam o cálculo das grandezas eletromagnéticas. A definição de um problema exterior para modelar a estrutura coaxial permite a análise dos campos dispersos nas extremidades e aumenta a precisão do cálculo da capacitância. Palavras-chave: axissimetria, campos elétricos, método dos elementos finitos, método variacional.The new generation of electromagnetic field simulators can be used for teaching electromagnetism with no user's deep knowledge about the methodology used to develop these computer programs. The theory of the cylindrical coaxial line is used to illustrate the application of these programs as teaching tools. The analytical solution of the problem is used to assess the accuracy of the numerical results produced by different subdivisions of the finite element meshes. The relationship between energy minimality and distribution of electric potentials is used to explain how different discretizations of the model affect the computation of the electromagnetic variables. The definition of an exterior problem to model the coaxial structure allows the analysis of leakage fields at the end-zone and improves the accuracy of capacitance calculation.

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“…One of the primary applications of non-orthogonal coordinates is the modelling of infinite domains (Lowther et al, 1989). In the electrostatic or magnetostatic case as well as in the eddy current case, the solution decreases to zero at infinity.…”

Section: Problems With Open Boundary Conditionsmentioning

confidence: 99%

Geometrical transformations and equivalent materials in computational electromagnetism

Nicolet

Zolla

Agha

et al. 2008

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -This paper aims to review various techniques used in computational electromagnetism such as the treatment of open problems, helicoidal geometries and the design of arbitrarily shaped invisibility cloaks. This seemingly heterogeneous list is unified by the concept of geometrical transformation that leads to equivalent materials. The practical set-up is conveniently effected via the finite element method. Design/methodology/approach -The change of coordinates is completely encapsulated in the material properties. Findings -The most significant examples are the simple 2D treatment of helicoidal geometries and the design of arbitrarily shaped invisibility cloaks. Originality/value -The paper provides a unifying point of view, bridging several techniques in electromagnetism.Keywords Computational electromagnetism, Helicoidal geometry, Photonic Crystal Fibre, Metamaterial, Invisibility cloaking Paper type Research paper 1. Geometrical transformations and equivalent materials Beside Cartesian coordinates, cylindrical and spherical coordinates, and even the other orthogonal systems (Stratton, 1941), have been commonly used to set up electromagnetic problems. In this paper, much more general coordinate systems are discussed since they do not need to be orthogonal (and not even real valued). A modern approach is to write the equations of electromagnetism in the language of exterior calculus that is covariant, i.e. independent of the choice of the coordinate system (Bossavit, 1991). In this way, the Maxwell equations involve only the exterior derivative and are purely topological and differential while all the metric information is contained in the material properties via a Hodge star operator. This looks rather abstract but can nevertheless be encapsulated in a very simple and practical equivalence rule (Milton et al., 2006;Zolla et al., 2005):When you change your coordinate system, all you have to do is to replace your initial material (electric permittivity tensor ¼ 1 and magnetic permeability tensor ¼ m) properties by equivalent material properties given by the following rule:2T detðJÞ andwhere J is the Jacobian matrix of the coordinate transformation consisting of the partial derivatives of the new coordinates with respect to the original ones (J 2 T is the transposed of its inverse).

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A sparse matrix open boundary method for finite element analysis

Cited by 60 publications

References 7 publications

Parametric Models in Quasi-Static Electromagnetics

Parametric Models in Quasi-Static Electromagnetics

Análise de cabos coaxiais cilíndricos usando a técnica dos elementos finitos

Geometrical transformations and equivalent materials in computational electromagnetism

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