Algebraic analysis of two-level multigrid methods for edge elements

Artem Napov (1) , Ronan Perrussel (2)

1 ULB - Université libre de Bruxelles
2 LAPLACE-GRE - Groupe de Recherche en Electromagnétisme

We present an algebraic analysis of two-level multigrid methods for the solution of linear systems arising from the discretization of the curl-curl boundary value problem with edge elements. The analysis is restricted to the singular compatible linear systems as obtained by setting to zero the contribution of the lowest order (mass) term in the associated partial differential equation. We use the analysis to show that for some discrete curl-curl problems, the convergence rate of some Reitzinger-Schöberl two-level multigrid variants is bounded independently of the mesh size and the problem peculiarities. This covers some discretizations on Cartesian grids, including problems with isotropic coefficients, anisotropic coefficients and/or stretched grids, and jumps in the coefficients, but also the discretizations on uniform unstructured simplex grids.

Mots clés: convergence analysis; multigrid; algebraic multigrid; two-level multigrid; Reitzinger-Schöberl multigrid; preconditioning; aggregation; edge elements AMS subject classifications 65N55; 65N12; 65N22; 35Q60

Domaines: Electromagnétisme; Analyse numérique [cs.NA]; Modélisation et simulation; Analyse numérique [math.NA]

Artem Napov, Ronan Perrussel. Algebraic analysis of two-level multigrid methods for edge elements. Electronic Transactions on Numerical Analysis, 2019, 51, pp.387-411. ⟨10.1553/etna_vol51s387⟩. ⟨hal-02388986⟩