Node placement for triangular mesh generation by Monte Carlo simulation

A new approach of node placement for unstructured mesh generation is proposed. It is based on the Monte Carlo method to position nodes for triangular or tetrahedral meshes. Surface or volume geometries to be meshed are treated as atomic systems, and mesh nodes are considered as interacting particles...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2005-10, Vol.64 (7), p.973-989
Main Authors: Zhang, Hanzhou, Smirnov, Andrei V.
Format: Article
Language:English
Subjects:
Computational techniques
Computer simulation
Exact sciences and technology
Finite element method
Finite-element and galerkin methods
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical methods in physics
Mesh generation
Monte Carlo methods
Monte Carlo simulation
node placement
Physics
Placement
Potential energy
Three dimensional
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Summary:A new approach of node placement for unstructured mesh generation is proposed. It is based on the Monte Carlo method to position nodes for triangular or tetrahedral meshes. Surface or volume geometries to be meshed are treated as atomic systems, and mesh nodes are considered as interacting particles. By minimizing system potential energy with Monte Carlo simulation, particles are placed into a near‐optimal configuration. Well‐shaped triangles or tetrahedra can then be created after connecting the nodes by constrained Delaunay triangulation or tetrahedrization. The algorithm is simple, easy to implement, and works in an almost identical way for 2D and 3D meshing. Copyright © 2005 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.1402