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Measuring the conformity of non‐simplicial elements to an anisotropic metric field
Author(s) -
Sirois Yannick,
Dompierre Julien,
Vallet MarieGabrielle,
Guibault François
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.1437
Subject(s) - measure (data warehouse) , mathematics , hexahedron , metric (unit) , quadrilateral , conformity , field (mathematics) , mathematical analysis , dimension (graph theory) , geometry , finite element method , pure mathematics , computer science , data mining , engineering , structural engineering , operations management , law , political science
This paper extends an approach for measuring the element conformity of simplices to non‐simplicial elements of any type, in spaces of arbitrary dimension. Element non‐conformity is defined as the difference between a given size specification map, in the form of a Riemannian metric tensor, and the actual metric tensor of the element. An approach to the measurement of non‐conformity coefficients of non‐simplicial elements based on sub‐simplex division is proposed. An analysis of the measure's behaviour presented for quadrilaterals, hexahedra, prisms and pyramids shows that the measure is sensitive to size, stretching and orientation variations, as well as to other types of element shape degeneration. Finally, numerical applications show that the metric conformity measure can be used as a quality measure to quantify the discrepancy between a whole non‐simplicial mesh and a complex anisotropic size specification map. Copyright © 2005 John Wiley & Sons, Ltd.