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![Using the semantic operations to simplify the structure of the hexahedral mesh. a The original mesh generated by using the paving method and sweeping method. There are many singular vertices on the hex mesh. b The base complex [2] of the original mesh has 422 cubes; c the simplified hex mesh is generated after we merge the singular vertices on the surface mesh; d the base complex of the simplified mesh has 219 cubes](publication/337365304/figure/fig19/AS:960087594106890@1605914128424/Using-the-semantic-operations-to-simplify-the-structure-of-the-hexahedral-mesh-a-The.png)
Using the semantic operations to simplify the structure of the hexahedral mesh. a The original mesh generated by using the paving method and sweeping method. There are many singular vertices on the hex mesh. b The base complex [2] of the original mesh has 422 cubes; c the simplified hex mesh is generated after we merge the singular vertices on the surface mesh; d the base complex of the simplified mesh has 219 cubes
Source publication
This paper introduces topological operations for editing the singularity on a hex mesh while maintaining the connectivity of hexahedral mesh. The operations include (1) an enhanced column collapse operation that can avoid generating the poor-quality elements; (2) a column insertion operation that is the opposite operation of column collapse; (3) fo...
Citations
We present a set of operators to perform modifications, in particular collapses and splits, in volumetric cell complexes which are discretely embedded in a background mesh. Topological integrity and geometric embedding validity are carefully maintained. We apply these operators strategically to volumetric block decompositions, so-called T-meshes or base complexes, in the context of hexahedral mesh generation. This allows circumventing the expensive and unreliable global volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid maps. In essence, we reduce this step to simpler local cube mapping problems, for which reliable solutions are available. As a consequence, the robustness of the mesh generation process is increased, especially when targeting coarse or block-structured hexahedral meshes. We furthermore extend this pipeline to support feature alignment constraints, and systematically respect these throughout, enabling the generation of meshes that align to points, curves, and surfaces of special interest, whether on the boundary or in the interior of the domain.
This paper presents an improved method for optimizing the singularity structure of hexahedral meshes using various dual operations. Our approach aims at reducing element distortion by decomposing complex singular nodes into singular curves using high-quality sheet insertion at proper locations. Then, singular curves that meet the topological parallel requirements are paired to perform the semantic column operation, which eliminates the singular curves. Finally, the topological structure is further optimized by collapsing sheets, resulting in a valid hex-mesh with a simpler structure. Compared to existing hexahedral mesh simplification methods, our approach can generate higher quality meshes. Experimental results demonstrate the effectiveness of the proposed method.
Generating structured meshes is often an expensive process, limiting the use of high-fidelity numerical simulation methods for design, especially when the design is not yet fixed and design updates are likely. For hexahedral meshes generated by decomposing a B-Rep model into regions for which simple meshing strategies are known, robustly propagating design modifications to the decomposed representation and subsequent mesh is very challenging. In this paper, an approach is presented to propagate parametric update and feature changes to structured meshes. Geometric and topological modifications on the design model are identified first, enabling the equivalent modifications to be identified on the decomposition of the design model. Virtual topology operations used to generate the initial decomposition are combined with the meshing constraints of individual sub-regions to update the decomposition and associated mesh locally. The approach is demonstrated for a number of design updates.
In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post processing algorithms for connectivity editing and mesh optimization. For each technique, we highlight capabilities and limitations, also pointing out the associated unsolved challenges. Recent relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.
In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post processing algorithms for connectivity editing and mesh optimization. For each technique, we highlight capabilities and limitations, also pointing out the associated unsolved challenges. Recent relaxed approaches, aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The required background, pertaining to geometrical as well as combinatorial aspects, is introduced along the way.
