Anomalous Magnetization Spikes in the Locally Corrected Nyström Discretization of Static Volume Integral Equation using Tetrahedral Cells

Authors

  • John C. Young Department of Electrical & Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA
  • Robert J. Adams Department of Electrical & Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA
  • Stephen D. Gedney Department of Electrical Engineering, University of Colorado – Denver, Denver, Colorado 80204, USA

DOI:

https://doi.org/10.13052/2024.ACES.J.390210

Keywords:

integral equation methods, locally corrected Nyström method, moment method

Abstract

A locally corrected Nyström (LCN) discretization of a magnetostatic volume integral equation is presented. Anomalous magnetization spikes can occur when the underlying mesh uses tetrahedral cells regardless of discretization order. The mechanism for the anomalous magnetization spikes is discussed, and mitigation of the spikes through use of an LCN-to-Moment Method conversion is investigated. Results are presented validating that the LCN-to-Moment Method suppresses the anomalous spikes.

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Author Biographies

John C. Young, Department of Electrical & Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA

John C. Young received the B.E.E. degree in electrical engineering from Auburn University in 1997, the M.S. degree in electrical engineering from Clemson University in 2000, and the Ph.D. degree in electrical engineering also from Clemson University in 2002.

From January 2003 to April 2003, he served as a post-doctoral researcher at Clemson University, and from 2003 to 2005, he served as a post-doctoral researcher at Tokyo Institute of Technology, Tokyo, Japan. From 2005 to 2008, he worked at Japan Radio Co. Since 2008, he has been with the Department of Electrical and Computer Engineering at the University of Kentucky, Lexington, KY where he is currently an associate professor.

Dr. Young’s research interests include integral equation methods, finite element methods, electromagnetic theory, waveguides, array antennas, and magnetic signature modeling of hysteretic materials. He is a member of IEEE, the Applied Electromagnetics Society (ACES), and URSI Commission B. He currently serves as an Associate Editor for the IEEE Transactions on Antennas and Propagation and on the Education Committee of the Antennas and Propagation Society. He also served (2020-2023) on the Board of Directors of ACES where he is currently Secretary.

Robert J. Adams, Department of Electrical & Computer Engineering, University of Kentucky, Lexington, Kentucky 40506, USA

Robert J. Adams received the B.S. degree from Michigan Technological University, Houghton, MI, USA, in 1993, and the M.S. and Ph.D. degrees in electrical engineering from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, VA, USA, in 1995 and 1998, respectively.

From 1999 to 2000, he was a Research Assistant Professor with Virginia Tech. Dr. Adams joined the University of Kentucky in 2001, where he is currently a Professor with the Department of Electrical and Computer Engineering.

He has made novel contributions to mesh and frequency stable integral equation formulations of electromagnetic problems, constraint-based methods for high-order MOM discretizations, spectral splitting methods for implementing shadowing effects in integral equations at high frequencies, and sparse direct solution methods for low-to-moderate frequency electromagnetics applications. Dr. Adams is a senior member of the IEEE.

Stephen D. Gedney, Department of Electrical Engineering, University of Colorado – Denver, Denver, Colorado 80204, USA

Stephen D. Gedney received the B.Eng.-Honors degree from McGill University, Montreal, P.Q., in 1985, and the M.S. and Ph.D. degrees in Electrical Engineering from the University of Illinois, Urbana-Champaign, IL, in 1987 and 1991, respectively.

He is currently the Don and Karen White Professor of the Department of Electrical Engineering at the University of Colorado Denver (CUD). Previously he was a Professor of Electrical Engineering at the University of Kentucky from 1991 – 2014. He worked for the U.S. Army Corps of Engineers, Champaign, IL (’85-’87). He was a visiting Professor at the Jet Propulsion Laboratory, (92’, 93’), HRL laboratories (’96-’97) and Alpha Omega Electromagnetics (’04-’05). He received the Tau Beta Pi Outstanding Teacher Award in 1995 and 2013. From 2002 – 2014, he was the Reese Terry Professor of Electrical and Computer Engineering at the University of Kentucky. He was titled as a Distinguished Professor of the University of Colorado in 2022. He is a past Associate Editor of the IEEE Transactions on Antennas and Propagation (1997 – 2004), a member of the IEEE Antennas and Propagation Society ADCOM (2000 – 2003), and served as the chair of the IEEE Antennas and Propagation Society Membership Committee (1995 – 2002). He is a Fellow of the IEEE and member of Tau Beta Pi.

References

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J. C. Young and S. D. Gedney, “A Locally Corrected Nyström formulation for the magnetostatic volume integral equation,” IEEE Transactions on Magnetics, vol. 47, no. 9, pp. 2163-2170, Sep. 2011.

J. C. Young, R. J. Adams, and S. D. Gedney, “Anomalous current spikes in the kocally corrected Nyström discretization of volume integral equations,” 2023 International Applied Computational Electromagnetics Society Symposium, Denver, CO, March 26-March 30, 2023.

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R. A. Pfeiffer, J. C. Young, R. J. Adams, and S. D. Gedney, “Locally corrected Nyström to moment method conversion for volume integral equations,” IEEE Transactions on Magnetics, vol. 55, no. 4, pp. 1-7, 2019.

M. Shafieipour, I. Jeffrey, J. Aronsson, and V. I. Okhmatovski, “On the equivalence of RWG method of moments and the locally corrected Nyström method for solving the electric field integral equation,” IEEE Transactions on Antennas and Propagation, vol. 62, no. 2, pp. 772-782, Feb. 2014.

R. D. Graglia and A. F. Peterson, Higher-Order Techniques in Computational Electromagnetics, Sci-Tech Publishing, 2016.

S. D. Gedney, A. Zhu, and C.-C. Lu, “Study of mixed-order basis functions for the locally corrected Nyström method,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 11, pp. 2996-3004, Nov. 2004.

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Published

2024-02-29

How to Cite

[1]
J. C. Young, R. J. Adams, and S. D. Gedney, “Anomalous Magnetization Spikes in the Locally Corrected Nyström Discretization of Static Volume Integral Equation using Tetrahedral Cells”, ACES Journal, vol. 39, no. 02, pp. 169–175, Feb. 2024.

Issue

2024: Vol 39 Iss 2

Section

ACES-Monterey 2023

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