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Lattice cleaving: a multimaterial tetrahedral meshing algorithm with guarantees.

Jonathan Bronson1, Joshua A Levine1, Ross Whitaker1

  • 1University of Utah, Salt Lake City.

IEEE Transactions on Visualization and Computer Graphics
|December 21, 2013
PubMed
Summary
This summary is machine-generated.

We present a new algorithm for creating high-quality tetrahedral meshes for multi-material volumetric domains. This method ensures geometric accuracy and allows for efficient mesh grading, optimizing element counts.

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Area of Science:

  • Computational geometry
  • Numerical analysis
  • Materials science

Background:

  • Generating accurate and efficient meshes is crucial for simulating complex physical phenomena.
  • Existing methods often struggle with multi-material domains or lack guarantees on mesh quality.
  • Volumetric meshing requires conforming to intricate physical boundaries.

Purpose of the Study:

  • To introduce a novel algorithm for generating tetrahedral meshes in multi-material volumetric domains.
  • To ensure the generated meshes possess high quality and geometric fidelity.
  • To enable efficient mesh construction and grading for reduced element counts.

Main Methods:

  • A combinatoric algorithm for tetrahedral mesh generation.
  • Implementation ensures upper and lower bounds on dihedral angles.
  • Method guarantees geometric fidelity to physical boundaries.
  • Mesh structure supports element grading in homogeneous regions.

Main Results:

  • The algorithm successfully generates high-quality tetrahedral meshes for arbitrary numbers of materials.
  • Proofs confirm bounded element quality and geometric fidelity.
  • The combinatoric nature allows for rapid mesh construction.
  • Mesh grading effectively reduces element count in homogeneous areas.

Conclusions:

  • The proposed algorithm offers a robust solution for tetrahedral meshing in complex multi-material domains.
  • It provides guarantees on mesh quality and geometric accuracy.
  • The method's efficiency and grading capability are significant advantages for computational simulations.