A consistency condition for the vector potential in multiply-connected domains
Classical Physics
2015-06-04 v1 Numerical Analysis
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.
Cite
@article{arxiv.1203.3993,
title = {A consistency condition for the vector potential in multiply-connected domains},
author = {Charles L. Epstein and Zydrunas Gimbutas and Leslie Greengard and Andreas Klöckner and Michael O'Neil},
journal= {arXiv preprint arXiv:1203.3993},
year = {2015}
}