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Mathematical modelling of multi conductor cables
1. | POEMS, INRIA - CNRS:UMR7231 - ENSTA ParisTech, ENSTA ParisTech, 828 Boulevard des Maréchaux, 91762 Palaiseau, France, France |
2. | M3DISIM, INRIA, Alan Turing, 1 rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France |
References:
[1] |
I. Aganovic and Z. Tutek, A justification of the one-dimensional model of elastic beam, Math. Methods in Applied Sci., 8 (1986), 1-14.
doi: 10.1002/mma.1670080133. |
[2] |
C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains, Mathematical Methods in the Applied Sciences, 21 (1998), 823-864.
doi: 10.1002/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B. |
[3] |
A. Bermúdez, D. Gómez and P. Salgado, Mathematical Models and Numerical Simulation in Electromagnetism, Springer, 2013.
doi: 10.1007/978-3-319-02949-8. |
[4] |
G. Canadas, Speed of Propagation of Solutions of a Linear Integro-differential Equation with Nonconstant Coefficients, SIAM Journal on Mathematical Analysis, 16 (1985), 143.
doi: 10.1137/0516009. |
[5] |
B. Cockburn and P. Joly, Maxwell equations in polarizable media, SIAM Journal on Mathematical Analysis, 19 (1988), 1372-1390.
doi: 10.1137/0519101. |
[6] |
R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, 3, Springer-Verlag, 1990. |
[7] |
M. Delfour and J. P. Zolésio, Shapes and Geometries. Analysis, Differential Calculus, and Optimization, Advances in Design and Control SIAM, Philadelphia, PA, 2001. |
[8] |
V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer-Verlag 1986.
doi: 10.1007/978-3-642-61623-5. |
[9] |
S. Imperiale and P. Joly, Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section,, Applied Num. Mathematics, ().
doi: 10.1016/j.apnum.2013.03.011. |
[10] |
S. Imperiale and P. Joly, Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section, Advances in Applied Mathematics and Mechanics, (AAMM), 4 (2012), 647-664. |
[11] |
P. Monk, Finite Element Methods for Maxwell's Equations, Oxford science publications, 2003.
doi: 10.1137/0729045. |
[12] |
C. R. Paul, Analysis of Multiconductor Transmission Lines, 2nd. New York 2008.
doi: 10.1109/9780470547212. |
[13] |
J. Stratton, Electromagnetic Theory, second printing ed., Mcgraw Hill, 1941. |
[14] |
M. F. Veiga, Asymptotic method applied to a beam with a variable cross section, in Asymptotic Methods for Elastic Structures (Lisbon, 1993), de Gruyter, Berlin, 1995, 237-254. |
[15] |
W. T. Weeks, Calculation of Coefficients of Capacitance of Multiconductor Transmission Lines in the Presence of a Dielectric Interface, IEEE Trans. MTT, 18 (1970), 35-43.
doi: 10.1109/TMTT.1970.1127130. |
[16] |
W. T. Weeks, Multiconductor transmission line theory in the TEM approximation, IBM Journal of Research and Development, (1972), 604-611.
doi: 10.1147/rd.166.0604. |
show all references
References:
[1] |
I. Aganovic and Z. Tutek, A justification of the one-dimensional model of elastic beam, Math. Methods in Applied Sci., 8 (1986), 1-14.
doi: 10.1002/mma.1670080133. |
[2] |
C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains, Mathematical Methods in the Applied Sciences, 21 (1998), 823-864.
doi: 10.1002/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B. |
[3] |
A. Bermúdez, D. Gómez and P. Salgado, Mathematical Models and Numerical Simulation in Electromagnetism, Springer, 2013.
doi: 10.1007/978-3-319-02949-8. |
[4] |
G. Canadas, Speed of Propagation of Solutions of a Linear Integro-differential Equation with Nonconstant Coefficients, SIAM Journal on Mathematical Analysis, 16 (1985), 143.
doi: 10.1137/0516009. |
[5] |
B. Cockburn and P. Joly, Maxwell equations in polarizable media, SIAM Journal on Mathematical Analysis, 19 (1988), 1372-1390.
doi: 10.1137/0519101. |
[6] |
R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, 3, Springer-Verlag, 1990. |
[7] |
M. Delfour and J. P. Zolésio, Shapes and Geometries. Analysis, Differential Calculus, and Optimization, Advances in Design and Control SIAM, Philadelphia, PA, 2001. |
[8] |
V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer-Verlag 1986.
doi: 10.1007/978-3-642-61623-5. |
[9] |
S. Imperiale and P. Joly, Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section,, Applied Num. Mathematics, ().
doi: 10.1016/j.apnum.2013.03.011. |
[10] |
S. Imperiale and P. Joly, Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section, Advances in Applied Mathematics and Mechanics, (AAMM), 4 (2012), 647-664. |
[11] |
P. Monk, Finite Element Methods for Maxwell's Equations, Oxford science publications, 2003.
doi: 10.1137/0729045. |
[12] |
C. R. Paul, Analysis of Multiconductor Transmission Lines, 2nd. New York 2008.
doi: 10.1109/9780470547212. |
[13] |
J. Stratton, Electromagnetic Theory, second printing ed., Mcgraw Hill, 1941. |
[14] |
M. F. Veiga, Asymptotic method applied to a beam with a variable cross section, in Asymptotic Methods for Elastic Structures (Lisbon, 1993), de Gruyter, Berlin, 1995, 237-254. |
[15] |
W. T. Weeks, Calculation of Coefficients of Capacitance of Multiconductor Transmission Lines in the Presence of a Dielectric Interface, IEEE Trans. MTT, 18 (1970), 35-43.
doi: 10.1109/TMTT.1970.1127130. |
[16] |
W. T. Weeks, Multiconductor transmission line theory in the TEM approximation, IBM Journal of Research and Development, (1972), 604-611.
doi: 10.1147/rd.166.0604. |
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