## $${\mathbf H}$$(curl) auxiliary mesh preconditioning.(English)Zbl 1212.65490

Summary: This paper analyses a two-level preconditioning scheme for $${\mathbf H}$$(curl) bilinear forms. The scheme utilizes an auxiliary problem on a related mesh that is more amenable for constructing optimal order multigrid methods. More specifically, we analyse the case when the auxiliary mesh only approximately covers the original domain. The latter assumption is important since it allows for an easy construction of nested multilevel spaces on regular auxiliary meshes. Numerical experiments in both two and three space dimensions illustrate the optimal performance of the method.

### MSC:

 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 35J25 Boundary value problems for second-order elliptic equations 65F08 Preconditioners for iterative methods 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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