Auxiliary Space AMG for H(curl) Problems

The search for efficient preconditioners for H(curl) problems on unstructured meshes has intensified in the last few years. The attempts to directly construct AMG (algebraic multigrid) methods had some success, see [10, 1, 6]. Exploiting available multilevel methods on auxiliary mesh for the same bilinear form led to efficient auxiliary mesh preconditioners to unstructured problems as shown in [7, 4]. A computationally more attractive approach was recently announced in [5]. Their method borrows the main tool from the above mentioned auxiliary mesh preconditioners, namely, the interpolation operator Π _h that maps functions from H(curl) into the lowest order Nédélec finite element space V _h . The method of [5] and its motivation are outlined in Section 2. In particular, we describe briefly their Nédélec space decomposition, which is the basis of the auxiliary space AMG preconditioners.