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arXiv · 2112.11080

Agglomeration-based geometric multigrid schemes for the Virtual Element Method

Paola Francesca Antonietti·Stefano Berrone·Martina Busetto·Marco Verani
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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 $C^0$-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.

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Paola Francesca Antonietti, Stefano Berrone, Martina Busetto, Marco Verani. 2021-12-21. Agglomeration-based geometric multigrid schemes for the Virtual Element Method. https://arxiv.org/abs/2112.11080

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