MDEC: MeTiS-based Domain Decomposition for Parallel 2D Mesh Generation

Abstract

Abstract Domain decomposition methods are commonly employed within the context of parallel numerical algorithms. Most often, the domain decomposition is performed before the main computation begins. Within the context of mesh generation, parallel mesh generation is desired when the goal is to mesh a very large geometric domain or if very high accuracy is required. In this paper, we propose a novel technique, which we call the MeTiS-based Domain Decomposition (MDEC) technique, for the decomposition of geometric domains into subdomains for use in parallel 2D mesh generation. Our technique is based upon discrete domain decomposition [1]. The algorithm proceeds by first constructing a background mesh which satisfies a minimum angle constraint of 30 degrees and second partitioning this initial coarse mesh or background mesh into subdomains. Finally, adjustments are applied to the triangles with small boundary angles so that all subdomains in the final decomposition contain boundary angles no smaller than 60 degrees which is a guaranteed property of the domain decomposition algorithm. We prove this guarantee for the boundary angles of the MDEC domain decomposition. Our results show that, in comparison to the medial axis domain decomposition (MADD) algorithm [2], our method provides a better balance of subdomain areas, better boundary angles, and a faster decomposition time. In addition, when the MDEC and MADD subdomains are used in conjunction with a parallel constained Delaunay mesh generation technique (PCDM) [3], the meshes are generated in approximately the same time and have very similar element quality.