Domain Decomposition for Mean Curvature Flow of Surface Polygonal Meshes

TL;DR

This paper explores domain decomposition techniques, including optimized Schwarz methods, to improve the efficiency of mean curvature flow computations on surface polygonal meshes, enabling parallel processing and shape quality analysis.

Contribution

It introduces adapted Robin transmission conditions for Schwarz methods and analyzes their impact on shape quality and texture deformation during mesh processing.

Findings

Decomposition allows parallel processing of mesh smoothing tasks.

Optimized Schwarz methods improve computational efficiency.

Shape quality and texture deformation are affected by the decomposition approach.

Abstract

We examine the use of domain decomposition for potentially more efficient mean curvature flow of surface meshes, whose faces are arbitrary simple polygons. We first test traditional domain decomposition methods with and without overlap of deconstructed domains. And we present adapted Robin transmission conditions of optimized Schwarz method. We then analyze the resulting smoothing from the point of view of shape quality and texture deformation. By decomposing the initial mesh into two sub-meshes, we solve two smaller boundary value problems instead of one big problem, and we can process these two tasks almost entirely in parallel.