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Title: Variational, stable, and self-consistent 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 arbitrary-geometry 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 self-consistent 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 non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM 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 O-wave in a rectilinear prismmore » and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole convolute.« less

Authors:
 [1];  [1]; ORCiD logo [1];  [1]
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  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), 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):
SAND-2021-14867J
Journal ID: ISSN 0021-9991; 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 0021-9991
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 self-consistent 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.
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McGregor, Duncan, Phillips, Edward, Sirajuddin, David, & Pointon, Timothy. Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain. United States. https://doi.org/10.1016/j.jcp.2021.110856
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McGregor, Duncan, Phillips, Edward, Sirajuddin, David, and Pointon, Timothy. Thu . "Variational, stable, and self-consistent 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.
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@article{osti_1834107,
title = {Variational, stable, and self-consistent 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 arbitrary-geometry 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 self-consistent 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 non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM 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 O-wave in a rectilinear prism and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole 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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https://doi.org/10.1016/j.jcp.2021.110856
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