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

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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.

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Acknowledgements

AOB acknowledges the support provided by Universidad de Chile through the “Programa VID Ayuda de Viaje 2017” and the Chilean National Fund for Scientific and Technological Development (FONDECYT) through grant CONICYT/FONDECYT No. 1181192. The work of CA is supported by CONICYT-PCHA/Magíster Nacional/2016-22161437. NHK is grateful for the support provided by the Chilean National Fund for Scientific and Technological Development (FONDECYT) through grant CONICYT/FONDECYT No. 1181506.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Universidad de Chile, Av. Beauchef 851, Santiago, 8370456, Chile

    A. Ortiz-Bernardin, C. Alvarez, R. Silva-Valenzuela & E. Olate-Sanzana

  2. Computational and Applied Mechanics Laboratory, Center for Modern Computational Engineering, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Av. Beauchef 851, Santiago, 8370456, Chile

    A. Ortiz-Bernardin, R. Silva-Valenzuela & E. Olate-Sanzana

  3. Department of Computer Science, Universidad de Chile, Av. Beauchef 851, Santiago, 8370456, Chile

    C. Alvarez & N. Hitschfeld-Kahler

  4. Meshing for Applied Science Laboratory, Center for Modern Computational Engineering, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Av. Beauchef 851, Santiago, 8370456, Chile

    N. Hitschfeld-Kahler

  5. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, 20153, Milano, Italy

    A. Russo

  6. Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, via Ferrata 1, 27100, Pavia, Italy

    A. Russo

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  1. A. Ortiz-Bernardin
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  2. C. Alvarez
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  5. R. Silva-Valenzuela
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  6. E. Olate-Sanzana
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Correspondence to A. Ortiz-Bernardin.

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Ortiz-Bernardin, A., Alvarez, C., Hitschfeld-Kahler, N. et al. Veamy: an extensible object-oriented C++ library for the virtual element method. Numer Algor 82, 1189–1220 (2019). https://doi.org/10.1007/s11075-018-00651-0

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