An Efficient Numerical Method for Time Domain Electromagnetic Wave Propagation in Co-axial Cables

References

[1] M. Admane, M. Sorine and Q. Zhang, Inverse scattering for soft fault diagnosis in electric transmission lines, IEEE Trans. Antennas Propagation 59 (2011), 141–148. 10.1109/TAP.2010.2090462Search in Google Scholar

[2] J. Albella Martínez, S. Imperiale, P. Joly and J. Rodríguez, Numerical analysis of a method for solving 2D linear isotropic elastodynamics with traction free boundary condition using potentials and finite elements, Math. Comp. 90 (2021), no. 330, 1589–1636. 10.1090/mcom/3613Search in Google Scholar

[3] F. Auzanneau, Wire troubleshooting and diagnosis: Review and perspectives, Progr. Electromagnetics Res. B 49 (2013), Article ID 253279. 10.2528/PIERB13020115Search in Google Scholar

[4] G. Beck, Modélisation et étude mathématique de réseaux de câbles électriques. Modélisation et simulation, Ph.D. thesis, Université Paris-Saclay, 2016. Search in Google Scholar

[5] G. Beck, Computer-implemented method for reconstructing the topology of a network of cables, US patent n ∘ : US20200363462A. 16/638,451, 2020, 2017, https://patents.google.com/patent/US20200363462A1/en. Search in Google Scholar

[6] G. Beck, S. Imperiale and P. Joly, Mathematical modelling of multi conductor cables, Discrete Contin. Dyn. Syst. Ser. S 8 (2015), no. 3, 521–546. 10.3934/dcdss.2015.8.521Search in Google Scholar

[7] G. Beck, S. Imperiale and P. Joly, Asymptotic modelling of skin-effects in coaxial cables, Partial Differ. Equ. Appl. 1 (2020), no. 6, Paper No. 42. 10.1007/s42985-020-00043-xSearch in Google Scholar

[8] M. Bergot and M. Duruflé, High-order optimal edge elements for pyramids, prisms and hexahedra, J. Comput. Phys. 232 (2013), 189–213. 10.1016/j.jcp.2012.08.005Search in Google Scholar

[9] A. Burel, S. Imperiale and P. Joly, Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition, Numer. Anal. Appl. 5 (2012), no. 2, 136–143. 10.1134/S1995423912020061Search in Google Scholar

[10] J. Chabassier and S. Imperiale, Fourth-order energy-preserving locally implicit time discretization for linear wave equations, Internat. J. Numer. Methods Engrg. 106 (2016), no. 8, 593–622. 10.1002/nme.5130Search in Google Scholar

[11] J.-L. Coulomb, F.-X. Zgainski and Y. Marechal, A pyramidal element to link hexahedral, prismatic and tetrahedral edge finite elements, IEEE Trans. Magnetics 33 (1997), no. 2, 1362–1365. 10.1109/20.582509Search in Google Scholar

[12] S. Descombes, S. Lanteri and L. Moya, Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell’s equations, J. Sci. Comput. 56 (2013), no. 1, 190–218. 10.1007/s10915-012-9669-5Search in Google Scholar

[13] M. Hochbruck, T. Jahnke and R. Schnaubelt, Convergence of an ADI splitting for Maxwell’s equations, Numer. Math. 129 (2015), no. 3, 535–561. 10.1007/s00211-014-0642-0Search in Google Scholar

[14] M. Hochbruck and J. Leibold, An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions, Numer. Math. 147 (2021), no. 4, 869–899. 10.1007/s00211-021-01184-wSearch in Google Scholar

[15] M. Hochbruck and A. Sturm, Error analysis of a second-order locally implicit method for linear Maxwell’s equations, SIAM J. Numer. Anal. 54 (2016), no. 5, 3167–3191. 10.1137/15M1038037Search in Google Scholar

[16] S. Imperiale, Asymptotic analysis of abstract two-scale wave propagation problems, Working paper (2021), https://hal.inria.fr/hal-03306856. Search in Google Scholar

[17] S. Imperiale and P. Joly, Error estimates for 1D asymptotic models in coaxial cables with non-homogeneous cross-section, Adv. Appl. Math. Mech. 4 (2012), no. 6, 647–664. 10.4208/aamm.12-12S06Search in Google Scholar

[18] S. Imperiale and P. Joly, Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section, Appl. Numer. Math. 79 (2014), 42–61. 10.1016/j.apnum.2013.03.011Search in Google Scholar

[19] J. Lee and B. Fornberg, A split step approach for the 3-D Maxwell’s equations, J. Comput. Appl. Math. 158 (2003), no. 2, 485–505. 10.1016/S0377-0427(03)00484-9Search in Google Scholar

[20] J. Lee and B. Fornberg, Some unconditionally stable time stepping methods for the 3D Maxwell’s equations, J. Comput. Appl. Math. 166 (2004), no. 2, 497–523. 10.1016/j.cam.2003.09.001Search in Google Scholar

[21] J. Li, E. A. Machorro and S. Shields, Numerical study of signal propagation in corrugated coaxial cables, J. Comput. Appl. Math. 309 (2017), 230–243. 10.1016/j.cam.2016.07.003Search in Google Scholar

[22] P. Monk, Finite Element Methods for Maxwell’s Equations, Oxford University, New York, 2003. 10.1093/acprof:oso/9780198508885.001.0001Search in Google Scholar

[23] J.-C. Nédélec, Mixed finite elements in R 3 , Numer. Math. 35 (1980), no. 3, 315–341. 10.1007/BF01396415Search in Google Scholar

[24] C. R. Paul, Analysis of Multiconductor Transmission Lines, Wiley, New York, 2008. 10.1109/9780470547212Search in Google Scholar

[25] T. Rylander and A. Bondeson, Stability of explicit-implicit hybrid time-stepping schemes for Maxwell’s equations, J. Comput. Phys. 179 (2002), no. 2, 426–438. 10.1006/jcph.2002.7063Search in Google Scholar