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

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.