A consistency condition for the vector potential in multiply-connected domains

Charles L. Epstein; Zydrunas Gimbutas; Leslie Greengard; Andreas Klockner; Michael O'Neil

doi:10.1109/TMAG.2012.2223480

A consistency condition for the vector potential in multiply-connected domains

Charles L. Epstein, Zydrunas Gimbutas, Leslie Greengard, Andreas Klockner, Michael O'Neil

Mathematics

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

Abstract

A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental role. For multiply-connected conductors, at zero frequency, the standard boundary conditions on the tangential components of the magnetic field do not uniquely determine the vector potential. We describe a (gauge-invariant) consistency condition that overcomes this nonuniqueness and resolves a long-standing difficulty in inverting the magnetic field integral equation.

Original language	English (US)
Article number	6327672
Pages (from-to)	1072-1076
Number of pages	5
Journal	IEEE Transactions on Magnetics
Volume	49
Issue number	3
DOIs	https://doi.org/10.1109/TMAG.2012.2223480
State	Published - 2013

Keywords

Electromagnetic theory
Maxwell equations
electromagnetic (EM) scattering
magnetic field integral equation (MFIE)
multiply-connected domains

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Electrical and Electronic Engineering

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10.1109/TMAG.2012.2223480

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AU - O'Neil, Michael

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AB - A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental role. For multiply-connected conductors, at zero frequency, the standard boundary conditions on the tangential components of the magnetic field do not uniquely determine the vector potential. We describe a (gauge-invariant) consistency condition that overcomes this nonuniqueness and resolves a long-standing difficulty in inverting the magnetic field integral equation.

KW - Electromagnetic theory

KW - Maxwell equations

KW - electromagnetic (EM) scattering

KW - magnetic field integral equation (MFIE)

KW - multiply-connected domains

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A consistency condition for the vector potential in multiply-connected domains

Abstract

Keywords

ASJC Scopus subject areas

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