Optimal Dual Schemes for Adaptive Grid Based Hexmeshing

Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from adaptively refined grid is prominent approach to automatic hexmeshing, and requires ability restore all hex property around hanging nodes that arise at interface between cells having different size. The most advanced tools accomplish this task based on dualization. These approaches use topological schemes regularize valence inner vertices edges, such dualizing yields mesh. In paper we study in detail dual approach, propose four main contributions it: (i) enumerate possible transitions methods must be able handle, showing prior do not natively cover them; (ii) show internally asymmetric, therefore only their implementation ambiguous, but choices lead with singular structure; (iii) explore combinatorial space schemes, selecting minimum set covers configurations also simplest structure output hexmesh; (iv) enlarge class adaptive grids can transformed into meshes, relaxing one tight requirements imposed by previous approaches, ultimately permitting obtain much coarser same geometric accuracy. Last least, first time make grid-based hexmeshing truly reproducible, releasing our code revealing conspicuous amount technical details were always overlooked literature, creating entry barrier was hard overcome practitioners field.