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

This paper summarizes the development of an object-oriented C++ library for the virtual element method (VEM) named Veamy, whose modular design is focused on its extensibility. The two-dimensional linear elastostatic problem has been chosen as the starting stage for the development of this library. In contrast to the standard finite element method, the VEM in two dimensions uses polygonal finite element meshes. The theory of the VEM in which Veamy is based upon is presented using a notation and a terminology that is commonly found in the finite element literature, thereby allowing potential users that are familiar with finite elements to understand and implement the virtual element method under the object-oriented paradigm. A complete sample usage of Veamy is provided for a cantilever beam subjected to a parabolic end load. A displacement patch test is also solved using Veamy. A third example features the interaction between Veamy and the polygonal mesh generator ∗Corresponding author. Tel: +56 (2) 297 846 64, Fax: +56 (2) 268 960 57, Email address: [email protected] (A. Ortiz-Bernardin)