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

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...

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Bibliographic Details
Published in:Numerical algorithms 2019-12, Vol.82 (4), p.1189-1220
Main Authors: Ortiz-Bernardin, A., Alvarez, C., Hitschfeld-Kahler, N., Russo, A., Silva-Valenzuela, R., Olate-Sanzana, E.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Approximation
C plus plus
C++ (programming language)
Code reuse
Computer Science
Decomposition
Elastostatics
Extensibility
Finite element analysis
Finite element method
Libraries
Linear algebra
Mesh generation
Methods
Modular design
Numeric Computing
Numerical Analysis
Object oriented programming
Open source software
Original Paper
Polygons
Public domain
Terminology
Theory of Computation
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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-018-00651-0