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PEMesh: a Graphical Framework for the Analysis of the InterplayBetween Geometry and PEM Solvers
arXiv - CS - Computational Geometry Pub Date : 2021-02-23 , DOI: arxiv-2102.11578
Daniela Cabiddu, Giuseppe Patanè, Michela Spagnuolo

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.

中文翻译:

PEMesh:用于分析几何和PEM解算器之间相互作用的图形框架

偏微分方程可以通过多面元方法(PEM)在一般的多边形和多面网格上求解。不幸的是,几何形状和分析之间的关系仍然未知,并且仍在进行中,以便确定较弱的形状规则性标准,从而使PEM能够可靠地工作。我们提出了PEMesh,这是一个图形框架,可支持对多边形网格的几何特性与PEM求解器的数值性能之间的关系进行分析。PEMesh允许通过利用任何外部PEM求解器来设计越来越强调某些几何特性的多边形网格,并支持对这种求解器的性能与输入网格的几何特性之间的相关性进行研究。此外,它是高度模块化的,可定制的,易于使用的,并提供了将分析结果导出为数值和图形图的可能性。PEMesh对正在进行和将来与PEM方法,多边形网格生成和处理有关的研究活动具有潜在的实际影响。
更新日期:2021-02-24
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