**Rudolf Beck**

This talk is about the solution of Maxwell's equations in the low
frequency range; the applications we aim at are implicit time-stepping
schemes for eddy current computations and the stationary double-curl
equation for time-harmonic fields. We assume that the computational
domain is discretized by Nédélec's
*H*(curl)-conforming edge
elements of the lowest order.

Algebraic coarsening strategies for such finite element spaces are harder to devise than in the case of Lagrange-type elements. The difficulties are basically due to the geometric structure of the vectorial shape functions.

The solution presented here relies on a spatial component splitting of the fields, where mesh coarsening takes place in an auxiliary subspace constructed with the aid of Lagrange-type basis functions. Within this subspace coarse grids are created recursively by an advancing-front algorithm, which merely exploits the matrix graphs.

Unfortunately, the non-trivial kernel of the curl-operator cannot be tackled within this setting. Thus we resort to a discrete Helmholtz decomposition of the fields, allowing an efficient smoothing of the kernel modes by a separate algebraic multigrid cycle.

Some numerical experiments will be presented in order to assess the efficacy of the proposed algorithms.