Vem++, a c++ library to handle and play with the Virtual Element Method

TL;DR

This paper introduces vem++, a C++ library designed to facilitate the implementation and experimentation of the Virtual Element Method (VEM) for solving PDEs on polytopal meshes, highlighting its design and capabilities.

Contribution

The paper presents vem++, a flexible C++ library that simplifies VEM implementation and extends its features for various PDE problems in multiple dimensions.

Findings

vem++ effectively handles 2D and 3D PDEs using VEM

The library supports integration of new quadrature rules and solvers

VEM implementation differs from FEM in handling polytopal meshes

Abstract

The Virtual Element Method (VEM) is an extension of the Finite Element Method (FEM) used for handling polytopal meshes. This paper provides a brief introduction to the VEM for a two-dimensional Laplacian problem. Additionally, it highlights the differences between a VEM implementation and a FEM code, emphasising the main challenges associated with the VEM. Furthermore, this paper presents a possible approach to address these challenges: vem++, a c++ library specifically developed for working with VEM discretisation. The library is designed to handle various partial differential equations in two or three dimensions, arising from both academic and engineering problems. Its flexible design allows for the seamless integration of new features, such as novel polytopes' quadrature rules, solvers, and virtual element spaces.