Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma

Bernd Hofmann; Thomas F. Eibert; Francesco P. Andriulli; Simon B. Adrian

doi:10.1109/APS/URSI47566.2021.9703799

Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma

Bernd Hofmann
, Thomas F. Eibert
, Francesco P. Andriulli
, Simon B. Adrian

Chair of High-Frequency Engineering

Technical University of Munich
Politecnico di Torino
University of Rostock

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

Integral equations become inaccurate in the low-frequency regime not only due to a low-frequency breakdown (i.e., growth of the condition number), but also due to catastrophic round-off errors in the discretization of the excitation. In this work, we propose a testing strategy for the excitation that results in a low-frequency stable discretization irrespective of the topology (i.e., simply- or multiply-connected) or orientability of the object. We obtain this by leveraging the lemma of Poincare to derive vector potentials for a general class of excitations. Numerical results demonstrate the effectiveness of our approach.

Original language	English
Title of host publication	2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	433-434
Number of pages	2
ISBN (Electronic)	9781728146706
DOIs	https://doi.org/10.1109/APS/URSI47566.2021.9703799
State	Published - 2021
Event	2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Singapore, Singapore Duration: 4 Dec 2021 → 10 Dec 2021

Publication series

Name	2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings

Conference

Conference	2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021
Country/Territory	Singapore
City	Singapore
Period	4/12/21 → 10/12/21

Access to Document

10.1109/APS/URSI47566.2021.9703799

Cite this

Hofmann, B., Eibert, T. F., Andriulli, F. P., & Adrian, S. B. (2021). Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma. In 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings (pp. 433-434). (2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/APS/URSI47566.2021.9703799

Hofmann, Bernd ; Eibert, Thomas F. ; Andriulli, Francesco P. et al. / Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma. 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2021. pp. 433-434 (2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings).

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title = "Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincar{\'e}'s Lemma",

abstract = "Integral equations become inaccurate in the low-frequency regime not only due to a low-frequency breakdown (i.e., growth of the condition number), but also due to catastrophic round-off errors in the discretization of the excitation. In this work, we propose a testing strategy for the excitation that results in a low-frequency stable discretization irrespective of the topology (i.e., simply- or multiply-connected) or orientability of the object. We obtain this by leveraging the lemma of Poincare to derive vector potentials for a general class of excitations. Numerical results demonstrate the effectiveness of our approach.",

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doi = "10.1109/APS/URSI47566.2021.9703799",

language = "English",

series = "2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings",

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Hofmann, B, Eibert, TF, Andriulli, FP & Adrian, SB 2021, Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma. in 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings. 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 433-434, 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021, Singapore, Singapore, 4/12/21. https://doi.org/10.1109/APS/URSI47566.2021.9703799

Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma. / Hofmann, Bernd; Eibert, Thomas F.; Andriulli, Francesco P. et al.
2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2021. p. 433-434 (2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma

AU - Hofmann, Bernd

AU - Eibert, Thomas F.

AU - Andriulli, Francesco P.

AU - Adrian, Simon B.

PY - 2021

Y1 - 2021

N2 - Integral equations become inaccurate in the low-frequency regime not only due to a low-frequency breakdown (i.e., growth of the condition number), but also due to catastrophic round-off errors in the discretization of the excitation. In this work, we propose a testing strategy for the excitation that results in a low-frequency stable discretization irrespective of the topology (i.e., simply- or multiply-connected) or orientability of the object. We obtain this by leveraging the lemma of Poincare to derive vector potentials for a general class of excitations. Numerical results demonstrate the effectiveness of our approach.

AB - Integral equations become inaccurate in the low-frequency regime not only due to a low-frequency breakdown (i.e., growth of the condition number), but also due to catastrophic round-off errors in the discretization of the excitation. In this work, we propose a testing strategy for the excitation that results in a low-frequency stable discretization irrespective of the topology (i.e., simply- or multiply-connected) or orientability of the object. We obtain this by leveraging the lemma of Poincare to derive vector potentials for a general class of excitations. Numerical results demonstrate the effectiveness of our approach.

UR - https://www.scopus.com/pages/publications/85126844590

U2 - 10.1109/APS/URSI47566.2021.9703799

DO - 10.1109/APS/URSI47566.2021.9703799

M3 - Conference contribution

AN - SCOPUS:85126844590

T3 - 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings

SP - 433

EP - 434

BT - 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021

Y2 - 4 December 2021 through 10 December 2021

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Hofmann B, Eibert TF, Andriulli FP, Adrian SB. Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma. In 2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2021. p. 433-434. (2021 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, APS/URSI 2021 - Proceedings). doi: 10.1109/APS/URSI47566.2021.9703799

Low-Frequency Stable Discretization of the Electric Field Integral Equation based on Poincaré's Lemma

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