# Algebraic Multigrid Methods For Virtual Element Discretizations: A Numerical Study

## 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.

## Key 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.