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Node placement for triangular mesh generation by Monte Carlo simulation
Author(s) -
Zhang Hanzhou,
Smirnov Andrei V.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1402
Subject(s) - delaunay triangulation , monte carlo method , tetrahedron , polygon mesh , node (physics) , triangulation , mesh generation , position (finance) , triangle mesh , computer science , topology (electrical circuits) , algorithm , computational science , geometry , finite element method , mathematics , engineering , computer graphics (images) , combinatorics , structural engineering , statistics , finance , economics
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.