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Related Experiment Video

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Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

A LAGUERRE VORONOI BASED SCHEME FOR MESHING PARTICLE SYSTEMS.

Chandrajit Bajaj¹

¹Center for Computational Visualization, Department of Computer Sciences, & Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712, http://www.cs.utexas.edu/users/bajaj.

Japan Journal of Industrial and Applied Mathematics

|September 28, 2011

Summary

This study introduces Laguerre Voronoi subdivision algorithms for creating high-quality quadrilateral and hexahedral meshes for particle systems. These methods ensure smooth, differentiable meshes suitable for various scientific simulations.

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Area of Science:

Computational geometry
Scientific computing
Meshing algorithms

Background:

Particle systems are fundamental in simulating physical phenomena.
Generating high-quality conformal meshes for particle systems is computationally challenging.
Existing methods often struggle with complex particle geometries and dynamic changes.

Purpose of the Study:

To develop novel Laguerre Voronoi based subdivision algorithms for quadrilateral and hexahedral meshing.
To create particle-conforming, smooth, and differentiable meshes for 2D and 3D particle systems.
To extend the algorithms for dynamic re-meshing scenarios.

Main Methods:

Utilizing Laguerre Voronoi diagrams to partition bounded regions containing particles.
Decomposing Voronoi cells into initial quadrilateral/hexahedral scaffolds.
Applying recursive subdivision techniques with specific averaging rules for mesh refinement.

Main Results:

Generation of particle-conforming quadrilateral and hexahedral meshes.
Meshes exhibit good quality, smoothness, and differentiability.
Demonstrated extensions for dynamic re-meshing (particle addition, deletion, movement).

Conclusions:

The proposed Laguerre Voronoi based subdivision algorithms provide an effective approach for meshing particle systems.
The resulting meshes are suitable for applications in composite materials, molecular dynamics, and astrophysics.
The dynamic re-meshing capabilities enhance the algorithms' utility in evolving simulations.