Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in order to identify weaker shape-regularity criteria under which PEMs can reliably work. We propose PEMesh, a graphical framework to support the analysis of the relation between the geometric properties of polygonal meshes and the numerical performances of PEM solvers. PEMesh allows the design of polygonal meshes that increasingly stress some geometric properties, by exploiting any external PEM solver, and supports the study of the correlation between the performances of such a solver and geometric properties of the input mesh. Furthermore, it is highly modular, customisable, easy to use, and provides the possibility to export analysis results both as numerical values and graphical plots. PEMesh has a potential practical impact on ongoing and future research activities related to PEM methods, polygonal mesh generation and processing.
翻译:部分差异方程式可以通过多面元素法(PEMS)解决在普通多边形和多面形介质上的部分差异方程。 不幸的是,几何和分析之间的关系仍不为人所知,而且需要不断进行研究,以便确定PEMs可以可靠地工作的较弱的形状常规性标准。我们提议PEMEsh,这是一个图形化框架,用以支持对多边形藻的几何特性与PEM解析器的数字性能之间的关系进行分析。PEMESE允许通过利用任何外部的PEM解答器来设计日益强调某些几何特性的多边形模类,并支持研究这种求解器的性能与输入网的几何性能之间的相互关系。此外,它具有高度模块性、自定义性、易于使用,并提供了输出分析结果的可能性,既包括数值和图形图。PEMM方法、聚形介质生成和处理,PEMESESE对当前和今后的研究活动可能产生实际影响。