Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T09:31:20.657Z Has data issue: false hasContentIssue false
  • English
  • Français

Error Estimates for 1D Asymptotic Models in Coaxial Cables with Non-Homogeneous Cross-Section

Published online by Cambridge University Press:  03 June 2015

Sébastien Imperiale  and
Patrick Joly
Sébastien Imperiale*
Affiliation:
Department of Applied Physics and Applied Mathematics, Columbia University, NY 10027, USA INRIA Rocquencourt, POems, domaine de Voluceau, 78153 Le Chesnay, France
Patrick Joly*
Affiliation:
INRIA Rocquencourt, POems, domaine de Voluceau, 78153 Le Chesnay, France
*
Email: si2245@columbia.edu
Corresponding author. Email: patrick.joly@inria.fr
Get access

Abstract

This paper is the first contribution towards the rigorous justification of asymptotic 1D models for the time-domain simulation of the propagation of electromagnetic waves in coaxial cables. Our general objective is to derive error estimates between the “exact” solution of the full 3D model and the “approximate” solution of the 1D model known as the Telegraphist’s equation.

Keywords

35L0535A3573R0535A40Coaxial cablesTelegraphist’s equationerror estimatesnon-homogeneous cross-section
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 6 , December 2012 , pp. 647 - 664
Copyright
Copyright © Global-Science Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Caorsi, S., Fernandes, P. and Raffetto, M., On the convergence of Galerkin finite element approximations of electromagnetic eigenproblems, SIAM J. Numer. Anal., 38(2) (2000), pp. 580–607.Google Scholar
[2]Dautray, R. and Lions, J. L., Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 3, Springer-Verlag, 1990.Google Scholar
[3]Hill, D. A. and Wait, J. R., Propagation along a Coaxial-Cable with a helical shield, IEEE Trans. Microwave Theory Tech., 28(2) (1980), pp. 84–89.Google Scholar
[4]Imperiale, S. and Joly, P., Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section, submitted, pp. 1–25.Google Scholar
[5]Imperiale, S. and Joly, P., Mathematical and numerical modelling of piezoelectric sensors, ESAIM: Math. Model. Numer. Anal., (46) (2012), pp. 875–909.CrossRefGoogle Scholar
[6]Joly, P., Variational methods for time dependant wave propagation, in Ainsworth, M., Davies, P., Duncan, D., Martin, P. and Rynne, B., editors, Topics in computational wave propagation: Direct and Inverse Problems, Computational Methods in Wave Propagation, pp. 201–264, Springer Verlag, October 2003.Google Scholar
[7]Monk, P., Finite Element Methods for Maxwell’s Equations, Oxford Science Publications, 2003.Google Scholar
[8]Rose, C. and Gans, M. J., A dielectric-free superconducting coaxial-cable, IEEE Trans. Microwave Theory Tech., 38(2) (1990), pp. 166–177.CrossRefGoogle Scholar
[9]Schmerr, L. W. Jr. and Song, S. J., Ultrasonic Nondestructive Evaluation Systems, Springer, 2007.Google Scholar