The Reduced Basis Multigrid scheme for the Virtual Element Method

TL;DR

This paper introduces a multigrid scheme for the Virtual Element Method that employs a reduced basis approach to efficiently compute intergrid operators on polygonal meshes, enhancing computational performance.

Contribution

It proposes a novel multigrid scheme using a reduced basis method to avoid implicit virtual space definitions, improving efficiency in VEM computations.

Findings

Efficient multigrid scheme for VEM on polygonal meshes

Reduced basis approach simplifies intergrid operator computation

Improved computational performance demonstrated

Abstract

We present a non-nested W-cycle multigrid scheme for the lowest order Virtual Element Method on polygonal meshes. To avoid the implicit definition of the Virtual Element space, which poses several issues in the computation of intergrid operators that underpin multigrid methods, the proposed scheme uses a fully-conforming auxiliary space constructed by cheaply computing the virtual basis functions via the reduced basis method.