Agglomeration-based geometric multigrid schemes for the Virtual Element Method

94/2021

Agglomeration-based geometric multigrid schemes for the Virtual Element Method

Monday 27th December 2021

Antonietti, P.F.; Berrone, S.; Busetto, M.; Verani, M.

In this paper we analyse the convergence properties of two-level, W-cycle and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear system of equations stemming from the lowest order C0-conforming Virtual Element discretization of two-dimensional second-order elliptic partial differential equations. The sequence of agglomerated tessellations are nested, but the corresponding multilevel virtual discrete spaces are generally non-nested thus resulting into non-nested multigrid algorithms. We prove the uniform convergence of the two-level method with respect to the mesh size and the uniform convergence of the W-cycle and the V-cycle multigrid algorithms with respect to the mesh size and the number of levels. Numerical experiments confirm the theoretical findings.