Hexahedral Meshing With Varying Element Sizes

Abstract

Hexahedral (or Hex‐) meshes are preferred in a number of scientific and engineering simulations and analyses due to their desired numerical properties. Recent state‐of‐the‐art techniques can generate high‐quality hex‐meshes. However, they typically produce hex‐meshes with uniform element sizes and thus may fail to preserve small‐scale features on the boundary surface. In this work, we present a new framework that enables users to generate hex‐meshes with varying element sizes so that small features will be filled with smaller and denser elements, while the transition from smaller elements to larger ones is smooth, compared to the octree‐based approach. This is achieved by first detecting regions of interest (ROIs) of small‐scale features. These ROIs are then magnified using the as‐rigid‐as‐possible deformation with either an automatically determined or a user‐specified scale factor. A hex‐mesh is then generated from the deformed mesh using existing approaches that produce hex‐meshes with uniform‐sized elements. This initial hex‐mesh is then mapped back to the original volume before magnification to adjust the element sizes in those ROIs. We have applied this framework to a variety of man‐made and natural models to demonstrate its effectiveness.

HexBox: Interactive Box Modeling of Hexahedral Meshes

“…The most widely‐studied fully automatic approaches explored by the computer graphics community in recent years employ adaptive grids [GSP19,PLC*21,LPC22,Mar09], polycubes [XGDC17, GSZ11, LVS*13, FXB16, FBL16, CLS16, MCBC22, DPM*22, GLYL20, HJS*14], or frame fields [NRP11, LLX*12, JHW*13, LZC*18, KLF16, SVB17, CC19, PBS20, BBC22]. Grid‐based approaches are versatile and unconditionally robust, but lack fine control on mesh quality and are prone to creating meshes with poor geometry and topology [LPC22].…”

Generalized adaptive refinement for grid-based hexahedral meshing

“…Specifically, Hu et al [2016] fit an octree in polycube space, and use ideas from Maréchal [2009] to restore the all-hex connectivity. Conversely, other approaches like [Cherchi et al 2019;Xu et al 2017] keep the sampling grid fixed, and enlarge or shrink portions of the polycube to obtain the wanted adaptivity. Our method can be seamlessly incorporated in the first approach, granting a lower element count, and is superior to the latter, which imposes that the singular structure of the mesh does not change, thus limiting the ability to adapt the mesh to features that are not present in polycube space (Section 6.2).…”