A Graphical Framework to Study the Correlation between Geometric Design and Simulation

TL;DR

PEMesh is a flexible graphical framework designed to analyze how the geometric properties of polygonal meshes influence the performance of Polytopal Element Methods (PEMs), aiding the development of more reliable mesh designs.

Contribution

It introduces PEMesh, a modular and customizable tool that links mesh geometry with PEM solver performance, facilitating research on shape-regularity criteria and mesh generation.

Findings

Supports analysis of geometric influence on PEM performance

Enables design of meshes with targeted geometric properties

Provides visual and numerical analysis outputs

Abstract

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.