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

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number6327672
Pages (from-to)1072-1076
Number of pages5
JournalIEEE Transactions on Magnetics
Volume49
Issue number3
DOIs
StatePublished - 2013

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Magnetic fields
Gages
Integral equations
Electric fields
Topology
Boundary conditions

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials

Cite this

A consistency condition for the vector potential in multiply-connected domains. / Epstein, Charles L.; Gimbutas, Zydrunas; Greengard, Leslie; Klockner, Andreas; O'Neil, Michael.

In: IEEE Transactions on Magnetics, Vol. 49, No. 3, 6327672, 2013, p. 1072-1076.

Research output: Contribution to journalArticle

Epstein, Charles L. ; Gimbutas, Zydrunas ; Greengard, Leslie ; Klockner, Andreas ; O'Neil, Michael. / A consistency condition for the vector potential in multiply-connected domains. In: IEEE Transactions on Magnetics. 2013 ; Vol. 49, No. 3. pp. 1072-1076.
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