AHF: Array-Based Half-Facet Data Structure for Mixed-Dimensional and Non-manifold Meshes

Abstract

We present an Array-based Half-Facet mesh data structure, or AHF, for efficient mesh query and modification operations. The AHF extends the com-pact array-based half-edge and half-face data structures (T.J. Alumbaugh and X. Jiao, Compact array-based mesh data structures, IMR, 2005) to support mixed-dimensional and non-manifold meshes. The design goals of our data structure in-clude generality to support such meshes, efficiency of neighborhood queries and mesh modification, compactness of memory footprint, and facilitation of interop-erability of mesh-based application codes. To accomplish these goals, our data structure uses sibling half-facets as a core abstraction, coupled with other explicit and implicit representations of entities. A unique feature of our data structure is a comprehensive implementation in MATLAB, which allows rapid prototyping, debugging, testing, and deployment of meshing algorithms and other mesh-based numerical methods. We have also developed C++ implementation built on top of MOAB (T.J. Tautges, R. Meyers, and K. Merkley, MOAB: A Mesh-Oriented Database, Sandia National Laboratories, 2004). We present some comparisons of the memory requirements and computational costs, and also demonstrate its effec-tiveness with a few sample applications.