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5 results on '"Telegrapher's models"'

1. Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models

Author

Geoffrey Beck and Akram Beni Hamad

Subjects
coaxial cables, maxwell's equations, telegrapher's models, finite elements, asymptotic analysis, Mathematics, QA1-939
Abstract

This work deals with wave propagation into a coaxial cable, which can be modelled by the 3D Maxwell equations or 1D simplified models. The usual model, called the telegrapher's model, is a 1D wave equation of the electrical voltage and current. We derived a more accurate model from the Maxwell equations that takes into account dispersive effects. These two models aim to be a good approximation of the 3D electromagnetic fields in the case where the thickness of the cable is small. We perform some numerical simulations of the 3D Maxwell equations and of the 1D simplified models in order to validate the usual model and the new one. Moreover, we show that, while the usual telegrapher model is of order one with respect to the thickness of the cable, the dispersive 1D model is of order two.

Published
2024
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2. Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparison between 3D and 1D models.

Author

Beck, Geoffrey and Hamad, Akram Beni

Subjects
COAXIAL cables, MAXWELL equations, ELECTROMAGNETIC fields, WAVE equation, THEORY of wave motion, ELECTROMAGNETIC wave propagation
Abstract

This work deals with wave propagation into a coaxial cable, which can be modelled by the 3D Maxwell equations or 1D simplified models. The usual model, called the telegrapher's model, is a 1D wave equation of the electrical voltage and current. We derived a more accurate model from the Maxwell equations that takes into account dispersive effects. These two models aim to be a good approximation of the 3D electromagnetic fields in the case where the thickness of the cable is small. We perform some numerical simulations of the 3D Maxwell equations and of the 1D simplified models in order to validate the usual model and the new one. Moreover, we show that, while the usual telegrapher model is of order one with respect to the thickness of the cable, the dispersive 1D model is of order two. [ABSTRACT FROM AUTHOR]

Published
2024
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3. An Efficient Numerical Method for Time Domain Electromagnetic Wave Propagation in Co-axial Cables.

Author

Beni Hamad, Akram, Beck, Geoffrey, Imperiale, Sébastien, and Joly, Patrick

Subjects
COAXIAL cables, MAXWELL equations, ELECTROMAGNETIC wave propagation, QUADRATURE domains, PRISMS
Abstract

In this work, we construct an efficient numerical method to solve 3D Maxwell's equations in coaxial cables. Our strategy is based upon a hybrid explicit-implicit time discretization combined with edge elements on prisms and numerical quadrature. One of the objectives is to validate numerically generalized telegrapher's models that are used to simplify the 3D Maxwell equations into a 1D problem. This is the object of the second part of the article. [ABSTRACT FROM AUTHOR]

Published
2022
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4. Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparaison between 3D and 1D models

Author

Beck, Geoffrey, Beni Hamad, Akram, Multi-scale numerical geometric schemes (MINGUS), École normale supérieure - Rennes (ENS Rennes)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Inria de Paris, and Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
[PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph], [SPI.ELEC]Engineering Sciences [physics]/Electromagnetism, Maxwell's equations, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Asymptotic analysis, Finite elements, Coaxial cables, Telegrapher's models, Numerical simulations, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Model's derivation, MSC: 35, 65 68
Abstract

International audience; This work deals with wave propagation into a coaxial cable, which can be modeled by the 3D Maxwell equations or 1D simplified models. The usual one, called the telegrapher's model, is a 1D wave equation on the electrical voltage and current. We derived a more accurate model from the Maxwell equations that takes into account dispersive effects. These two models aim to be a good approximation of the 3D electromagnetic fields in the case where the thinness of the cable is small. We perform some numerical simulations of the 3D Maxwell equations and of the 1D simplified models in order to validate the usual model and the new one. Moreover, we show that while the usual telegrapher model is of order one with respect to the thinness of the cable, the dispersive 1D model is of order two.

Published
2023

5. An efficient numerical method for time domain electromagnetic wave propagation in co-axial cables

Author

Akram Beni-Hamad, Geoffrey Beck, Sébastien Imperiale, Patrick Joly, Beck, Geoffrey, Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS-PSL), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)

Subjects
Computational Mathematics, Numerical Analysis, Edge elements, Hybrid numerical method, Applied Mathematics, Coaxial cables, Telegrapher's models, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Maxwell's equation, Numerical simulation, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this work, we construct an efficient numerical method to solve 3D Maxwell’s equations in coaxial cables. Our strategy is based upon a hybrid explicit-implicit time discretization combined with edge elements on prisms and numerical quadrature. One of the objectives is to validate numerically generalized telegrapher’s models that are used to simplify the 3D Maxwell equations into a 1D problem. This is the object of the second part of the article.

Published
2022

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