GPU Parallel algorithm for the generation of polygonal meshes based on terminal-edge regions

TL;DR

This paper introduces a GPU parallel algorithm for generating polygonal meshes from Delaunay triangulations, improving scalability and potential applications in virtual element methods.

Contribution

It presents a novel GPU-based approach for creating polygonal meshes from triangulations, including classification, polygon formation, and simplification processes.

Findings

Algorithm shows good scalability in experiments

Compared favorably with sequential algorithms

Meshes are useful for virtual element methods

Abstract

This paper presents a GPU parallel algorithm to generate a new kind of polygonal meshes obtained from Delaunay triangulations. To generate the polygonal mesh, the algorithm first uses a classification system to label each edge of an input triangulation; second it builds polygons (simple or not) from terminal-edge regions using the label system, and third it transforms each non-simple polygon from the previous phase into simple ones, convex or not convex polygons. We show some preliminary experiments to test the scalability of the algorithm and compare it with the sequential version. We also run a very simple test to show that these meshes can be useful for the virtual element method.