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Erschienen in:
Harmonic Balance with Small Signal Perturbation Kapitel lesen Erstes Kapitel lesen

2024 | OriginalPaper | Buchkapitel

Implementation and Validation of the Dual Full-Wave E and H Formulations with Electric Circuit Element Boundary Conditions

verfasst von : Gabriela Ciuprina, Daniel Ioan, Ruth V. Sabariego

Erschienen in: Scientific Computing in Electrical Engineering

Verlag: Springer Nature Switzerland

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Abstract

Dual full-wave (FW) frequency-domain \(\textbf{E}\) and \(\textbf{H}\) formulations, with scalar potentials on the boundary, and with electric circuit element boundary conditions are discussed and details about their implementation in the finite element method are given. For some magneto-quasi-static devices this duality frames the exact solution thus allowing the accuracy control. In such cases the geometric mean of the dual solutions exhibits a better accuracy and higher convergence rate than the individual numerical solutions. For FW devices the dual formulations allow a compromise between model accuracy and computational effort, especially if the models are not 3D. Implementation is available for free in onelab. Validation for test cases with analytic solution are provided: a conducting cylinder and a coaxial cable.

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Vorheriges Kapitel Matrix-Free Parallel Preconditioned Iterative Solvers for the 2D Helmholtz Equation Discretized with Finite Differences
Nächstes Kapitel A Yee-Like Finite Element Scheme for Maxwell’s Equations on Hybrid Grids with Mass-Lumping
Fußnoten
1
Classic to ECE: \(\oint _{\partial \varOmega } (\textbf{n} \times \mathbf {\underline{E}}_t) \cdot \mathbf {\underline{H}}^\prime \, \textrm{d}A = \int _{\varSigma } -( \textbf{n} \times \nabla _2 \underline{V}) \cdot \mathbf {\underline{H}}^\prime \, \textrm{d}A = \sum _{k=1}^m \underline{V}_k \oint _{\partial S_k} \textbf{H}_t^\prime \cdot \textbf{dl} = \sum _{k \in {\mathscr {I}}_v} \underline{V}_k I_k^\prime \).
 
2
Other resources are available at www.lmn.pub.ro/\(\sim \)gabriela/ece..
 
3
Here 2.5D was adopted as an acronym for the axisymmetric problems because from mathematical point of view the model is 2D, but from the physical point of view the model is 3D, no domain truncation is done along the azimuth direction. Numerically, this is encoded in the computation of the Jacobian [9]. This is different from plane-parallel 2D problems where the model is 2D both from mathematical and physical points of view, there is a domain truncation along the Oz axis (physical end effects are neglected).
 
4
Error convergence for uniform meshes of increasing fineness; h is the characteristic length of the element.
 
5
Three different computations are needed for the Richardson extrapolation, based on the assumption \(\underline{Z}(h) = \underline{Z}_0 + A h^p\), with \(\underline{Z}_0\), A and h unknowns. If the mesh sizes are such that \(h_1/h_2 = h_2/h_3\), the extrapolated value is computed as \(\underline{Z}_0 = (\underline{Z}_1 \underline{Z}_3 - \underline{Z}_2^2)/(\underline{Z}_1 - 2 \underline{Z}_2 + \underline{Z}_3)\), with \(\underline{Z}_k = \underline{Z}(h_k)\), \(k=1,2,3\).
 
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Henrotte, F., Meys, B., Hedia, H., Dular, P., Legros, W.: Finite element modelling with transformation techniues. IEEE Trans. Magn. 35(3), 1434–1437 (1999)CrossRef
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Steinmetz, T., Kurz, S., Clemens, M.: Domains of validity of quasistatic and quasistationary field approximations. COMPEL - Int. J. Comput. Math. Electr. Electron. Eng. 30(4), 1237–1247 (2011)MathSciNetCrossRef
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Wu, H., Cangellaris, A.C.: Model-order reduction of finite-element approximations of passive electromagnetic devices including lumped electrical-circuit models. IEEE Trans. Microwave Theory Tech. 52(9), 2305–2313 (2004)CrossRef
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Jochum, M., et al.: A new low-frequency stable potential formulation for the finite-element simulation of electromagnetic fields. IEEE Trans. Magn. 51(3), 1–4 (2015)CrossRef
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Metadaten
Titel
Implementation and Validation of the Dual Full-Wave E and H Formulations with Electric Circuit Element Boundary Conditions
verfasst von
Gabriela Ciuprina
Daniel Ioan
Ruth V. Sabariego
Copyright-Jahr
2024
Buch
Scientific Computing in Electrical Engineering

Print ISBN: 978-3-031-54516-0

Electronic ISBN: 978-3-031-54517-7

Copyright-Jahr: 2024

DOI
https://doi.org/10.1007/978-3-031-54517-7_8

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