Agglomeration-based geometric multigrid schemes for the Virtual Element Method

Code:
94/2021
Title:
Agglomeration-based geometric multigrid schemes for the Virtual Element Method
Date:
Monday 27th December 2021
Author(s):
Antonietti, P.F.; Berrone, S.; Busetto, M.; Verani, M.
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Abstract:
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.