Algebraic multigrid by component splitting for edge elements on simplicial triangulations

Our focus is on Maxwell’s equations in the low frequency range; two specific ap-plications we aim at are 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 triangles or tetrahedrons; for the finite el-ement approximation we choose Nedelec’s H[curl)-conforming edge elements of the lowest order. For the solution of the arising linear equation systems we devise an algebraic multi-grid preconditioner based on a spatial component splitting of the field. Mesh coars-ening takes place in an auxiliary subspace, which is constructed with the aid of a nodal vector basis. Within this subspace coarse grids are created by exploiting the matrix graphs. Additionally, we have to cope with the kernel of the cuW-operator, which comprises a considerable part of the spectral modes on the grid. Fortunately, the kernel modes are accessible via a discrete Helmholtz decomposition of the fields; they are smoothed by additional algebraic multigrid cycles. Numerical experiments are included in order to assess the efficacy of the proposed algorithms