Algebraic Multigrid Methods For Virtual Element Discretizations: A Numerical Study
Daniele Prada, Micol Pennacchio
TL;DR
This paper evaluates the effectiveness of algebraic multigrid methods in solving linear systems from Virtual Element discretizations on complex polygonal meshes, including cases with heterogeneous diffusion coefficients.
Contribution
It provides a comprehensive numerical study demonstrating the performance of algebraic multigrid methods for Virtual Element discretizations on general meshes.
Findings
Multigrid methods are effective for complex polygonal meshes.
Heterogeneous coefficients do not significantly impair convergence.
The study offers practical insights into solver performance for VEM discretizations.
Abstract
We investigate the performance of algebraic multigrid methods for the solution of the linear system of equations arising from a Virtual Element discretization. We provide numerical experiments on very general polygonal meshes for a model elliptic problem with and without highly heterogeneous diffusion coefficients and we draw conclusions regarding the efficacy of the method.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Computational Fluid Dynamics and Aerodynamics · Advanced Mathematical Modeling in Engineering