Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain

McGregor, Duncan; Phillips, Edward; Sirajuddin, David; Pointon, Timothy

doi:10.1016/j.jcp.2021.110856

Title: Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain

Journal Article · Thu Nov 18 00:00:00 EST 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110856· OSTI ID:1834107

McGregor, Duncan ^[1]; Phillips, Edward ^[1];

^[1]; Pointon, Timothy ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: NA0003525

OSTI ID:: 1834107

Report Number(s):: SAND-2021-14867J; 701962; TRN: US2300124

Journal Information:: Journal of Computational Physics, Vol. 451; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (16)

Review of pulsed power-driven high energy density physics research on Z at Sandia Sinars, D. B.; Sweeney, M. A.; Alexander, C. S. Physics of Plasmas, Vol. 27, Issue 7 https://doi.org/10.1063/5.0007476	journal	July 2020
Diagonally implicit Runge–Kutta methods for stiff ODEs Kennedy, Christopher A.; Carpenter, Mark H. Applied Numerical Mathematics, Vol. 146 https://doi.org/10.1016/j.apnum.2019.07.008	journal	December 2019
Transmission Line Theory for Field-to-Transmission Line Coupling Calculations lanoz, M.; Nucci, C. A.; Tesche, F. M. Electromagnetics, Vol. 8, Issue 2-4 https://doi.org/10.1080/02726348808908214	journal	January 1988
Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form Phillips, Edward G.; Shadid, John N.; Cyr, Eric C. SIAM Journal on Scientific Computing, Vol. 40, Issue 3 https://doi.org/10.1137/17M1135827	journal	January 2018
An Algebraic Multigrid Approach Based on a Compatible Gauge Reformulation of Maxwell's Equations Bochev, Pavel B.; Hu, Jonathan J.; Siefert, Christopher M. SIAM Journal on Scientific Computing, Vol. 31, Issue 1 https://doi.org/10.1137/070685932	journal	January 2008
Formulation of the field-to-transmission line coupling equations in terms of magnetic excitation field Rachidi, F. IEEE Transactions on Electromagnetic Compatibility, Vol. 35, Issue 3 https://doi.org/10.1109/15.277316	journal	January 1993
Dirichlet boundary value correction using Lagrange multipliers Burman, Erik; Hansbo, Peter; Larson, Mats G. BIT Numerical Mathematics, Vol. 60, Issue 1 https://doi.org/10.1007/s10543-019-00773-4	journal	September 2019
Kokkos: Enabling manycore performance portability through polymorphic memory access patterns Carter Edwards, H.; Trott, Christian R.; Sunderland, Daniel Journal of Parallel and Distributed Computing, Vol. 74, Issue 12 https://doi.org/10.1016/j.jpdc.2014.07.003	journal	December 2014
Modeling magnetically insulated devices using flow impedance Mendel, C. W.; Rosenthal, S. E. Physics of Plasmas, Vol. 2, Issue 4 https://doi.org/10.1063/1.871345	journal	April 1995
Dynamic modeling of magnetically insulated transmission line systems Mendel, C. W.; Rosenthal, S. E. Physics of Plasmas, Vol. 3, Issue 11 https://doi.org/10.1063/1.871553	journal	November 1996
A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier–Stokes equations Elman, Howard; Howle, V. E.; Shadid, John Journal of Computational Physics, Vol. 227, Issue 3 https://doi.org/10.1016/j.jcp.2007.09.026	journal	January 2008
A Review of Field-to-Transmission Line Coupling Models With Special Emphasis to Lightning-Induced Voltages on Overhead Lines Rachidi, Farhad IEEE Transactions on Electromagnetic Compatibility, Vol. 54, Issue 4 https://doi.org/10.1109/TEMC.2011.2181519	journal	August 2012
Plasma evolution and dynamics in high-power vacuum-transmission-line post-hole convolutes Rose, D. V.; Welch, D. R.; Hughes, T. P. Physical Review Special Topics - Accelerators and Beams, Vol. 11, Issue 6 https://doi.org/10.1103/PhysRevSTAB.11.060401	journal	June 2008
Using the Sherman-Morrison-Woodbury Formula for Coupling External Circuits With FEM for Simulation of Eddy Current Problems White, D. A. IEEE Transactions on Magnetics, Vol. 45, Issue 10 https://doi.org/10.1109/TMAG.2009.2022274	journal	October 2009
Numerical solution of saddle point problems Benzi, Michele; Golub, Gene H.; Liesen, Jörg Acta Numerica, Vol. 14 https://doi.org/10.1017/S0962492904000212	journal	April 2005
A Note on Preconditioning for Indefinite Linear Systems Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. SIAM Journal on Scientific Computing, Vol. 21, Issue 6 https://doi.org/10.1137/S1064827599355153	journal	January 2000

Similar Records

Application of Novel High Order Time Domain Vector Finite Element Method to Photonic Band-Gap Waveguides

Conference · Tue Jan 13 00:00:00 EST 2004 · OSTI ID:1834107

Rieben, R; White, D; Rodrigue, G

Parallel computation of electromagnetic fields

Technical Report · Wed May 21 00:00:00 EDT 1997 · OSTI ID:1834107

Madsen, N K

Investigations of Beam Dynamics Issues at Current and Future Hadron Accelerators (Final Report)

Technical Report · Thu Mar 12 00:00:00 EDT 2015 · OSTI ID:1834107

Ellison, James; Lau, Stephen; Heinemann, Klaus; +1 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Maxwell's equations
finite element methods
Lagrange multipliers
transmission line coupling
circuit coupling
code verification

Title: Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain

Citation Formats

References (16)

Similar Records

Related Subjects