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On the L 2 and the H 1 couplings for an overlapping domain decomposition method using Lagrange multipliers
Author(s) -
Guidault P.A.,
Belytschko T.
Publication year - 2006
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.1882
Subject(s) - lagrange multiplier , domain decomposition methods , coupling (piping) , cantilever , constraint algorithm , mortar methods , mathematics , mathematical analysis , multiplier (economics) , physics , mathematical optimization , finite element method , materials science , structural engineering , engineering , thermodynamics , macroeconomics , economics , metallurgy
In this paper, a comparison of the L 2 and the H 1 couplings is made for an overlapping domain decomposition method using Lagrange multipliers. The analysis of the local equations arising from the formulation of the coupling of two mechanical models shows that continuous weight functions are required for the L 2 coupling term whereas both discontinuous and continuous weight functions can be used for the H 1 coupling. The choice of the Lagrange multiplier space is discussed and numerically studied. The paper ends with some numerical examples of an end‐loaded cantilever beam and a cracked plate under tension and shear. It is shown that the continuity enforced with the H 1 coupling leads to a link with a flexibility that can be beneficial for coupling a very coarse mesh with a very fine one. To limit the effect of the volume coupling on the global response, a narrow coupling zone is recommended. In this case, volume coupling tends to a surface coupling, especially with a L 2 coupling. Copyright © 2006 John Wiley & Sons, Ltd.