In this paper we analyze 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 agglomerated tessellations in the sequence are nested, but the corresponding multilevel virtual discrete spaces are generally non-nested, thus resulting in 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.

AGGLOMERATION-BASED GEOMETRIC MULTIGRID SCHEMES FOR THE VIRTUAL ELEMENT METHOD

Antonietti P. F.;Berrone S.;Verani M.
2023-01-01

Abstract

In this paper we analyze 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 agglomerated tessellations in the sequence are nested, but the corresponding multilevel virtual discrete spaces are generally non-nested, thus resulting in 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.
2023
agglomeration
elliptic problems
geometric multigrid algorithms
polygonal meshes
virtual element method
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1237585
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