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arXiv · 1203.3993

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

Charles L. Epstein·Zydrunas Gimbutas·Leslie Greengard·Andreas Klöckner·Michael O'Neil
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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 non-uniqueness and resolves a longstanding difficulty in inverting the magnetic field integral equation.

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Charles L. Epstein, Zydrunas Gimbutas, Leslie Greengard, Andreas Klöckner, Michael O'Neil. 2012-03-18. A consistency condition for the vector potential in multiply-connected domains. https://doi.org/10.1109/tmag.2012.2223480

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