Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

• Published in: Computer aided design Vol. 85; pp. 68 - 82
• Main Authors: Ray, Navamita, Grindeanu, Iulian, Zhao, Xinglin, Mahadevan, Vijay, Jiao, Xiangmin
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.04.2017; Elsevier BV
• Subjects: Algorithms; Bandwidths; Computing time; Convergence; Data structures; Finite element method; Half-facet; Hierarchical meshes; Hierarchies; High-order surface reconstruction; Mathematical analysis; Multidimensional methods; Multigrid methods; Parallel computation; Projection; Reconstruction; Solvers; Uniform mesh refinement; Half-facet; Uniform mesh refinement; Parallel computation; Hierarchical meshes; High-order surface reconstruction
• ISSN: 0010-4485; 1879-2685; 1879-2685
• DOI: 10.1016/j.cad.2016.07.011

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE’s using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in-memory refinement). We also describe a high-order boundary reconstruction capability that can be used to project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries. The capability is developed under the parallel unstructured mesh framework “Mesh Oriented dAtaBase” (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. We also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems. •Multi-degree, multi-dimensional & multi-level unstructured mesh refinement framework.•Ecient parallel communication strategies for resolution of shared mesh interface.•High-order surface reconstruction based point projection schemes for mesh hierarchies.