Enhancing Hex-dominant Meshes: Generation, Evaluation, and Simplification

Hex-dominant mesh generation has recently received increasing attention from researchers and the simulation community due to its robustness compared to pure hex-mesh generation techniques. However, simulation algorithms require a limited number of cell types and mesh elements of desired quality to perform physics-based simulations over complex geometries. Unfortunately, in practice, most automatic hex-dominant generation algorithms for various geometries may contain unpredictable mesh elements, low-quality components, and undesired configurations. Furthermore, the hex-dominant meshing community lacks effective strategies for evaluating mesh structures or performing post-processing operations on these meshes. To address these challenges, this dissertation analyzed the demands aligned with the key stages in the meshing pipeline and contributed to the following areas: First, I designed a new hex-dominant mesh generation pipeline with an effective mesh extraction strategy. The generation pipeline links field information for feature alignment and utilizes a Voronoi diagram for geometry representation, which enables the pipeline to excel in both global and local controllability. The extraction strategy significantly improves generation performance. Second, I introduced a new 3D hexahedral mesh visual analysis system that highlights poor-quality areas with an aggregated glyph, emphasizes overlapping elements, and offers multi-level analysis through multiple views to effectively evaluate various mesh models and compare the performance of mesh generation and optimization algorithms for hex meshes. Third, I developed the first framework for analyzing hex-dominant meshes. It extends the base complex of pure hex-meshes by including non-hex elements. I also introduced a strategy to extract a cleaned (optimized) valence-based singularity graph wireframe to study the structure of both meshes and sheets. Fourth, I presented a first structure-informed simplification framework aimed at reducing the number of non-hex cells in hex-dominant meshes. My framework eliminates non-hex cells by using a novel relation graph that captures the connections involving edges and extracted sub-structures. I conducted comprehensive evaluations for each contribution, which demonstrated the advantages of my methods and their potential impact on related communities.

Name thesis:degree_name

Doctor of Philosophy

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Houston

Year dc:date.issued

2025

Author dc:creator

• Si, Lei 1995-

Advisor dc:contributor.advisor

• Chen, Guoning

Committee members dc:contributor.committeemember

• Mayerich, David
• Wu, Panruo
• Deng, Zhigang

• Computer science

Language dc:language.iso

English

Handle dc:identifier.uri

https://hdl.handle.net/10657/20686

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/20686