Conformal and non-conformal adaptive mesh refinement with hierarchical array-based half-facet data structures

We present a generalization of the Array-based Half-Facet (AHF) mesh data structure, called Hierarchical AHF, for hierarchical unstructured meshes generated from adaptive mesh refinement for solving PDEs. This data structure extends the AHF data structure (V. Dyedov, et al. AHF: Array-based Half-Facet Data Structure for Mixed-Dimensional and Non-manifold Meshes) to support meshes with hierarchical structure, which often are generated from adaptive mesh refinement (AMR). The design goals of our data structure include generality to support efficient neighborhood queries, refinement and derefinement, and hp-FEM with mesh smoothing. Our data structure utilizes the sibling half-facets as a core abstraction, coupled with a tree structure for hierarchical information. To facilitate the interoperability of mesh based applications, auxiliary data will be designed on top of Hierarchical AHF. We describe the data structure and software requirements, and present numerical experiments to demonstrate its effectiveness.