On the Low-Frequency Behavior of Vector Potential Integral Equations for Perfect Electrically Conducting Scatterers

Rui Chen; Huseyin Arda Ulku; Francesco P. Andriulli; Hakan Bagci

doi:10.1109/tap.2022.3210650

On the Low-Frequency Behavior of Vector Potential Integral Equations for Perfect Electrically Conducting Scatterers

Rui Chen, Huseyin Arda Ulku, Francesco P. Andriulli, Hakan Bagci

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Low-frequency behavior of vector potential integral equations (VPIEs) for perfect electrically conducting scatterers is investigated. Two equation sets are considered: The first set (VPIE-1) enforces the tangential component of the vector potential on the scatterer surface to be zero and uses the fundamental field relation on its normal component. The second set (VPIE-2) uses the same condition as VPIE-1 for the tangential component of the vector potential but enforces its divergence to be zero. In both sets, unknowns are the electric current and the normal component of the vector potential on the scatterer surface and are expanded using Rao-Wilton-Glisson (RWG) and pulse basis functions, respectively. To achieve a conforming discretization, RWG, scalar Buffa-Christiansen, and pulse testing functions are used. Theoretical and numerical analyses of the resulting matrix systems show that the electric current obtained by solving VPIE-1 has the wrong frequency scaling and is inaccurate at low frequencies.

Original language	English (US)
Pages (from-to)	1-1
Number of pages	1
Journal	IEEE Transactions on Antennas and Propagation
DOIs	https://doi.org/10.1109/tap.2022.3210650
State	Published - Oct 5 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-10-07
Acknowledged KAUST grant number(s): 2019-CRG8-4056
Acknowledgements: This work was supported in part by the National Natural Science Foundation of China under Grant 62201264, and in part by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No 2019-CRG8-4056.

ASJC Scopus subject areas

Electrical and Electronic Engineering
Condensed Matter Physics

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10.1109/tap.2022.3210650

https://repository.kaust.edu.sa/bitstream/10754/682259/1/On_the_Low-Frequency_Behavior_of_Vector_Potential_Integral_Equations_for_Perfect_Electrically_Conducting_Scatterers.pdf

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title = "On the Low-Frequency Behavior of Vector Potential Integral Equations for Perfect Electrically Conducting Scatterers",

abstract = "Low-frequency behavior of vector potential integral equations (VPIEs) for perfect electrically conducting scatterers is investigated. Two equation sets are considered: The first set (VPIE-1) enforces the tangential component of the vector potential on the scatterer surface to be zero and uses the fundamental field relation on its normal component. The second set (VPIE-2) uses the same condition as VPIE-1 for the tangential component of the vector potential but enforces its divergence to be zero. In both sets, unknowns are the electric current and the normal component of the vector potential on the scatterer surface and are expanded using Rao-Wilton-Glisson (RWG) and pulse basis functions, respectively. To achieve a conforming discretization, RWG, scalar Buffa-Christiansen, and pulse testing functions are used. Theoretical and numerical analyses of the resulting matrix systems show that the electric current obtained by solving VPIE-1 has the wrong frequency scaling and is inaccurate at low frequencies.",

author = "Rui Chen and Ulku, {Huseyin Arda} and Andriulli, {Francesco P.} and Hakan Bagci",

note = "KAUST Repository Item: Exported on 2022-10-07 Acknowledged KAUST grant number(s): 2019-CRG8-4056 Acknowledgements: This work was supported in part by the National Natural Science Foundation of China under Grant 62201264, and in part by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No 2019-CRG8-4056.",

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AU - Chen, Rui

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AU - Andriulli, Francesco P.

AU - Bagci, Hakan

N1 - KAUST Repository Item: Exported on 2022-10-07 Acknowledged KAUST grant number(s): 2019-CRG8-4056 Acknowledgements: This work was supported in part by the National Natural Science Foundation of China under Grant 62201264, and in part by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No 2019-CRG8-4056.

PY - 2022/10/5

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N2 - Low-frequency behavior of vector potential integral equations (VPIEs) for perfect electrically conducting scatterers is investigated. Two equation sets are considered: The first set (VPIE-1) enforces the tangential component of the vector potential on the scatterer surface to be zero and uses the fundamental field relation on its normal component. The second set (VPIE-2) uses the same condition as VPIE-1 for the tangential component of the vector potential but enforces its divergence to be zero. In both sets, unknowns are the electric current and the normal component of the vector potential on the scatterer surface and are expanded using Rao-Wilton-Glisson (RWG) and pulse basis functions, respectively. To achieve a conforming discretization, RWG, scalar Buffa-Christiansen, and pulse testing functions are used. Theoretical and numerical analyses of the resulting matrix systems show that the electric current obtained by solving VPIE-1 has the wrong frequency scaling and is inaccurate at low frequencies.

AB - Low-frequency behavior of vector potential integral equations (VPIEs) for perfect electrically conducting scatterers is investigated. Two equation sets are considered: The first set (VPIE-1) enforces the tangential component of the vector potential on the scatterer surface to be zero and uses the fundamental field relation on its normal component. The second set (VPIE-2) uses the same condition as VPIE-1 for the tangential component of the vector potential but enforces its divergence to be zero. In both sets, unknowns are the electric current and the normal component of the vector potential on the scatterer surface and are expanded using Rao-Wilton-Glisson (RWG) and pulse basis functions, respectively. To achieve a conforming discretization, RWG, scalar Buffa-Christiansen, and pulse testing functions are used. Theoretical and numerical analyses of the resulting matrix systems show that the electric current obtained by solving VPIE-1 has the wrong frequency scaling and is inaccurate at low frequencies.

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DO - 10.1109/tap.2022.3210650

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JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

ER -

On the Low-Frequency Behavior of Vector Potential Integral Equations for Perfect Electrically Conducting Scatterers

Abstract

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