Agglomeration-Based Geometric Multigrid Schemes for the Virtual Element Method
| Autor: | Paola F. Antonietti, Stefano Berrone, Martina Busetto, Marco Verani |
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| Rok vydání: | 2023 |
| Předmět: |
Numerical Analysis
Computational Mathematics agglomeration virtual element method Applied Mathematics FOS: Mathematics geometric multigrid algorithms agglomeration virtual element method elliptic problems polygonal meshes Mathematics - Numerical Analysis Numerical Analysis (math.NA) polygonal meshes elliptic problems geometric multigrid algorithms |
| Zdroj: | SIAM Journal on Numerical Analysis. 61:223-249 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/21m1466864 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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