Adaptive and Unstructured Mesh Cleaving

Area of Science:

• Computational geometry
• Computer-aided design
• Numerical analysis

Background:

• Adaptive tetrahedral meshing methods often struggle with geometric boundaries.
• Complex, non-manifold boundaries pose significant challenges for existing meshing techniques.
• Decoupling mesh quality from boundary conformity is crucial for robust simulations.

Purpose of the Study:

• To present a new strategy for boundary conforming meshing.
• To address the limitations of current methods in handling complex geometries.
• To improve the quality and conformity of tetrahedral meshes.

Main Methods:

• A novel strategy that decouples mesh generation from boundary conforming.
• Building a background mesh with desired tetrahedral properties.
• Utilizing a generalized stenciling method (cleaving) for boundary adherence.
• Developing new methods for graded tetrahedral meshes and generalizing existing algorithms.

Main Results:

• Successfully generates boundary conforming tetrahedral meshes.
• Maintains good element quality while adhering to complex boundaries.
• Introduces a generalized stenciling method applicable to unstructured meshes.

Conclusions:

• The proposed strategy effectively handles complex, non-manifold boundaries.
• This approach offers improved tetrahedral mesh generation for simulations.
• The technical contributions advance the field of adaptive meshing.