Variational, stable, and selfconsistent coupling of 3D electromagnetics to 1D transmission lines in the time domain
Abstract
This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrarygeometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. Here, we propose a selfconsistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to nonTEM modes on this boundary. We demonstrate that this feature reduces nonphysical reflection and ringing of nonTEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient Owave in a rectilinear prismmore »
 Authors:

 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1834107
 Report Number(s):
 SAND202114867J
Journal ID: ISSN 00219991; 701962; TRN: US2300124
 Grant/Contract Number:
 NA0003525
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 451; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Maxwell's equations; finite element methods; Lagrange multipliers; transmission line coupling; circuit coupling; code verification
Citation Formats
McGregor, Duncan, Phillips, Edward, Sirajuddin, David, and Pointon, Timothy. Variational, stable, and selfconsistent coupling of 3D electromagnetics to 1D transmission lines in the time domain. United States: N. p., 2021.
Web. doi:10.1016/j.jcp.2021.110856.
McGregor, Duncan, Phillips, Edward, Sirajuddin, David, & Pointon, Timothy. Variational, stable, and selfconsistent coupling of 3D electromagnetics to 1D transmission lines in the time domain. United States. https://doi.org/10.1016/j.jcp.2021.110856
McGregor, Duncan, Phillips, Edward, Sirajuddin, David, and Pointon, Timothy. Thu .
"Variational, stable, and selfconsistent coupling of 3D electromagnetics to 1D transmission lines in the time domain". United States. https://doi.org/10.1016/j.jcp.2021.110856. https://www.osti.gov/servlets/purl/1834107.
@article{osti_1834107,
title = {Variational, stable, and selfconsistent coupling of 3D electromagnetics to 1D transmission lines in the time domain},
author = {McGregor, Duncan and Phillips, Edward and Sirajuddin, David and Pointon, Timothy},
abstractNote = {This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrarygeometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. Here, we propose a selfconsistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to nonTEM modes on this boundary. We demonstrate that this feature reduces nonphysical reflection and ringing of nonTEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient Owave in a rectilinear prism and a steadystate problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Zmachine MITL and posthole convolute.},
doi = {10.1016/j.jcp.2021.110856},
journal = {Journal of Computational Physics},
number = ,
volume = 451,
place = {United States},
year = {2021},
month = {11}
}
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