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<p>The Virtual Element Method (VEM) is an extension of the Finite Element Method (FEM) to handle polytopal meshes. After giving a short introduction of the VEM for a two dimensional Laplacian problem, we show the differences between an implementation of a VEM and a FEM code highlighting which are the main issues associated with the VEM framework. Furthermore, this paper will show one of the possible ways to face such issues: <Emphasis FontCategory="NonProportional">Vem++</Emphasis> a <Emphasis FontCategory="NonProportional">C++</Emphasis> library developed to “deal and play” with the VEM discretisation. This <Emphasis FontCategory="NonProportional">C++</Emphasis> library deals with the VEM, since there are several partial differential equations in two/three dimensions coming from both academic and engineering problems. Then, one can “play” with the VEM, since <Emphasis FontCategory="NonProportional">Vem++</Emphasis> has been designed so that one can plug-in new features such as new polytopes quadrature rules, new solvers and new virtual element spaces in a smart way.</p>

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Vem++, a C++ library to handle and play with the virtual element method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月29日

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  • Franco Dassi

摘要

The Virtual Element Method (VEM) is an extension of the Finite Element Method (FEM) to handle polytopal meshes. After giving a short introduction of the VEM for a two dimensional Laplacian problem, we show the differences between an implementation of a VEM and a FEM code highlighting which are the main issues associated with the VEM framework. Furthermore, this paper will show one of the possible ways to face such issues: Vem++ a C++ library developed to “deal and play” with the VEM discretisation. This C++ library deals with the VEM, since there are several partial differential equations in two/three dimensions coming from both academic and engineering problems. Then, one can “play” with the VEM, since Vem++ has been designed so that one can plug-in new features such as new polytopes quadrature rules, new solvers and new virtual element spaces in a smart way.