Cabiddu, DanielaPatané, GiuseppeSpagnuolo, MichelaCabiddu, DanielaSchneider, TeseoAllegra, DarioCatalano, Chiara EvaCherchi, GianmarcoScateni, Riccardo2022-11-082022-11-082022978-3-03868-191-52617-4855https://doi.org/10.2312/stag.20221251https://diglib.eg.org:443/handle/10.2312/stag20221251Partial 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 to identify weaker shape-regularity criteria under which PEMs can reliably work. We propose a graphical framework to support the analysis of the relation between the geometric properties of polygonal meshes and the numerical performances of PEM solvers. Our framework, namely 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 the 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. The framework has a potential practical impact on ongoing and future research activities related to PEM methods, polygonal mesh generation and processing.Attribution 4.0 International LicenseCCS Concepts: Software and its engineering -> Open source model; Computing methodologies -> Mesh geometry models; Mathematics of computing -> Partial differential equationsSoftware and its engineeringOpen source modelComputing methodologiesMesh geometry modelsMathematics of computingPartial differential equations10.2312/stag.2022125111-199 pages