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Verification of three‐dimensional anisotropic adaptive processes
Author(s) -
Labbé Paul,
Dompierre Julien,
Vallet MarieGabrielle,
Guibault François
Publication year - 2011
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.3178
Subject(s) - polygon mesh , norm (philosophy) , isotropy , mathematical optimization , interpolation (computer graphics) , computer science , process (computing) , finite element method , algorithm , mathematics , geometry , artificial intelligence , motion (physics) , physics , quantum mechanics , political science , law , thermodynamics , operating system
A verification methodology for adaptive processes is devised. The mathematical claims made during the process are identified and measures are presented in order to verify that the mathematical equations are solved correctly. The analysis is based on a formal definition of the optimality of the adaptive process in the case of the control of the L ∞ ‐norm of the interpolation error. The process requires a reconstruction that is verified using a proper norm. The process also depends on mesh adaptation toolkits in order to generate adapted meshes. In this case, the non‐conformity measure is used to evaluate how well the adapted meshes conform to the size specification map at each iteration. Finally, the adaptive process should converge toward an optimal mesh. The optimality of the mesh is measured using the standard deviation of the element‐wise value of the L ∞ ‐norm of the interpolation error. The results compare the optimality of an anisotropic process to an isotropic process and to uniform refinement on highly anisotropic 2D and 3D test cases. Copyright © 2011 John Wiley & Sons, Ltd.