This paper studies numerical methods for eddy current problems in the case of homogeneous, isotropic, and linear materials. It provides a survey of approaches that entirely rely on boundary integral equations and their conforming Galerkin discretization. The pivotal role of potentials is discussed, as well as the topological issues raised by their use. Direct boundary integral equations and the so-called symmetric coupling of the integral equations corresponding to the conductor and the non-conducting regions is employed. It gives rise to coupled variational problems that are elliptic in suitable trace spaces. This implies quasi-optimal convergence of Galerkin boundary element schemes.
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