Adaptive and Quality Quadrilateral/Hexahedral Meshing from Volumetric Data.

Area of Science:

• Computational geometry
• Computer graphics
• Scientific visualization

Background:

• Generating high-quality volumetric meshes is crucial for accurate finite element simulations.
• Existing methods often struggle with adaptivity, boundary approximation, and preserving mesh quality.

Purpose of the Study:

• To develop an algorithm for direct extraction of adaptive and quality quadrilateral/hexahedral meshes from volumetric data.
• To enable user-controlled mesh adaptivity based on error functions, regions of interest, or simulation results.

Main Methods:

• A bottom-up, topology-preserving octree-based algorithm to determine the initial octree level.
• Dual contouring for preliminary uniform quad/hex mesh extraction.
• Adaptive decomposition of the mesh without introducing hanging nodes.
• Vertex position recalculation for accurate boundary surface approximation.
• A relaxation-based technique for mesh quality improvement.

Main Results:

• Successfully extracted adaptive and quality quadrilateral/hexahedral meshes directly from volumetric data.
• Demonstrated the algorithm's effectiveness across diverse application domains.
• Validated the utility of the generated meshes in finite element simulations.

Conclusions:

• The proposed algorithm provides an efficient and robust method for generating high-quality, adaptive volumetric meshes.
• The technique enhances simulation accuracy by improving boundary approximation and mesh quality.
• The generated meshes are suitable for demanding finite element analysis applications.