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Filling space with tetrahedra
Author(s) -
Naylor D. J.
Publication year - 1999
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/(sici)1097-0207(19990410)44:10<1383::aid-nme616>3.0.co;2-i
Subject(s) - tetrahedron , equilateral triangle , polygon mesh , context (archaeology) , cuboid , space (punctuation) , mathematics , finite element method , geometry , hexahedron , function (biology) , topology (electrical circuits) , computer science , combinatorics , structural engineering , engineering , geology , paleontology , evolutionary biology , biology , operating system
In the context of 3D finite element meshes various options for filling an indefinite space (such as would be approached within a fine mesh) with tetrahedra are considered. This problem is not trivial as it is in 2‐D since, unlike equilateral triangles, regular tetrahedra cannot be fitted together to fill space. Various groupings, or assemblies, which can be repeated indefinitely to fill space are considered. By altering the shape of the tetrahedra in one of these to minimize a suitable function a unique shape of tetrahedron is obtained which optimizes the conditioning. The mesh thus produced is shown to be better conditioned than alternatives based on assemblies of different shaped tetrahedra. A number of conditioning measures are used to confirm this. Finally, actual meshes which fit boundaries are briefly considered. Copyright © 1999 John Wiley & Sons, Ltd.