High-quality structured and semi-structured meshes are indispensable for achieving accurate and efficient numerical simulations in science, engineering, and medicine. The publications below highlight our research group's ongoing efforts to overcome fundamental challenges in 3D hexahedral meshing. By introducing innovative methodologies for global structure alignment, robust untangling, adaptive feature preservation, and topological simplification, we aim to bridge the gap between complex raw geometries and simulation-ready models tailored for Finite Element Analysis (FEA) and Isogeometric Analysis (IGA).
Hexahedral Mesh Optimization Approaches
Hexahedral Mesh Quality Improvement via Edge-Angle Optimization
Focus: Untangling and geometric quality enhancement (Computer & Graphics)
- Proposes a practical edge-angle optimization strategy to untangle and improve the geometric quality of hexahedral elements.
- Features a mathematically simpler formulation compared to existing methods, utilizing boundary surface deformation during the untangling phase.
- Significantly improves the Minimum Scaled Jacobian (MSJ) of the elements, yielding inversion-free deformations back to the original volume.
Structure Simplification of Hexahedral Meshes
Focus: Reducing mesh complexity via structural simplification (SIGGRAPH Asia 2017)
- Tackles the complexity of raw generated hex-meshes by simplifying their underlying singularity structure.
- Utilizes specialized sheet operations and topological adjustments to collapse unnecessary structural complexities.
- Enhances downstream analysis precision and efficiency, conserving storage space while retaining geometric fidelity.
Hexahedral Mesh Re-parameterization from Aligned Base-Complex
Focus: Global structure and base-complex optimization (SIGGRAPH 2015)
- Presents the first complete pipeline to optimize the global topological structure of a hex-mesh.
- Extracts the "base-complex" to study and rectify misalignments among structural singularities.
- Dramatically reduces the number of sub-components, making the resulting mesh highly suitable for Isogeometric Analysis (IGA) and spline fitting.
Hexahedral Mesh Quality Visualization and Analysis
A Visualization System for Hexahedral Mesh Quality Study
Focus: Effective visualization of element quality for hex-meshes (IEEE Vis 2023)
- Designs a glyph to aggregate and encode local element quality information for effective visualization.
- Implements a visual analytic system to allow a level-of-detail of hex element quality inspection.
- Conducts a user-study to evaluate the effectiveness of the proposed visualizations.
Hexahedral Mesh Structure Visualization and Evaluation
Focus: Decompose hex-mesh structure for effective visualization and quality analysis (IEEE SciVis 2018)
- Presents a robust techniquee to extract the base complex of a hex-mesh.
- Proposes a decomposition and reduction framework to reduce the visual complexity of base complex for effective visual representation.
- Introduces the first comprehensive metric to measure the complexity of base complex that considers the complexity of the relations among sub-structures.
Evaluating Hex-mesh Quality Metrics via Correlation Analysis
Focus: evaluating the effectiveness of different quality metrics for hex-mesh quality (SGP 2017/Computer Graphics Forum)
- Conducts a first massive and comprehensive evaluation using all available quality metrics on a large number of hex-meshes.
- Correlates these quality metrics with the simulation quality when solving a number of elliptic PDE problems on the individual hex-meshes.
- Suggested effective metrics for specific types of simulations from the evaluations and correlation study that may guide the development of future optimization techniques for hex-meshes.
Hexahedral Mesh Generation Approaches
Adaptive Hexahedral Mesh Generation
Focus: Varying element sizes for feature preservation (Computer Graphics Forum)
- Introduces a novel framework to generate hex-meshes with varying element densities without relying on standard octree structures.
- Allows small-scale regions of interest (ROI) to be magnified using As-Rigid-As-Possible (ARAP) deformations.
- Results in smooth transitions between dense elements (around features) and larger elements, guaranteeing high-quality volumetric outputs.
Structured Volume Decomposition via Generalized Sweeping
Focus: Volumetric decomposition for predictable and simple structured hex-meshes (IEEE TVCG)
- Introduces a novel volumetric decomposition technique based on generalized sweeping to generate structured hex-meshes.
- Constructs the mesh by matching and connecting 2D skeletal structures through adjacent level sets, with special attention paid to bifurcations.
- Emphasizes the creation of as few hexahedral components as possible to drastically reduce the number of extraordinary edges.
- Yields simple, predictable topologies that make fast computation and higher-order spline fitting significantly more achievable.
