VEMesh Dataset

This dataset contains the complete output of the performance and reproducibility studies for VEMesh, an open-source C++ library for quality-driven improvement of planar polygonal meshes. The studies quantify how VEMesh's two mesh-improvement primitives — element agglomeration and vertex relaxation — affect the conditioning of virtual element method (VEM) discretizations on polygonal meshes that arise when triangle and quadrilateral meshes are cut by embedded interfaces and boundaries. The data comprises four studies: a circular boundary clipped into a structured quadrilateral mesh over four refinement levels (circle/); five polygonal interfaces embedded in a fixed triangle mesh (shapes/); and the five benchmark polygonal meshes of Sorgente et al, J Comp. Phys.(2025) improved with a stability-based (sorgente/) and a shape-based (sorgente_shape/) quality metric. For the circle and shapes studies, each configuration is sampled over 1000 random mesh–geometry intersections, so the reported conditioning reflects a distribution of outcomes rather than a single case. For every mesh the archive provides the improved mesh (ASCII VTK), and per-study summary tables (CSV) giving the extremal eigenvalues and spectral condition number of the global VEM stiffness matrix for each of four improvement variants (baseline, agglomeration, relaxation, and their combination). Each directory includes a README.md documenting the file formats and the exact parameters used to generate the data. The VEMesh software that produced this dataset, including all generation and analysis scripts, is available at https://bitbucket.org/rram/vemesh. This dataset accompanies R. Rangarajan and N. Sukumar, CutVEM: Conforming virtual element method on embedded domains with shape-agnostic element agglomeration, Computer Methods in Applied Mechanics and Engineering 449 (2026) 118540.