Veamy: an extensible object-oriented C++ library for the virtual element method

TL;DR

Veamy is an object-oriented C++ library designed for the virtual element method, enabling flexible and extensible analysis of polygonal meshes in 2D elasticity and Poisson problems, with demonstrated performance and usability.

Contribution

This work introduces Veamy, a modular, extensible C++ library for VEM, bridging the gap between VEM and FEM with practical examples and performance comparisons.

Findings

Veamy effectively solves 2D elastostatic and Poisson problems.

The library demonstrates good extensibility and usability.

Performance comparison shows VEM's competitiveness with FEM.

Abstract

This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson problems in two dimensions have been chosen as the starting stage for the development of this library. The theory of the VEM, upon which Veamy is built, is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis. Several examples are provided to demonstrate the usage of Veamy, and in particular, one of them features the interaction between Veamy and the polygonal mesh generator PolyMesher. A computational performance comparison between VEM and FEM is also conducted. Veamy is free and open source software.