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A two‐scale approximation of the Schur complement and its use for non‐intrusive coupling
Author(s) -
Gendre L.,
Allix O.,
Gosselet P.
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.3142
Subject(s) - schur complement , complement (music) , domain decomposition methods , stiffness matrix , solver , coupling (piping) , scale (ratio) , context (archaeology) , finite element method , domain (mathematical analysis) , matrix (chemical analysis) , mathematics , computer science , mathematical optimization , mathematical analysis , structural engineering , engineering , physics , mechanical engineering , materials science , geography , chemistry , archaeology , composite material , biochemistry , quantum mechanics , eigenvalues and eigenvectors , complementation , gene , phenotype
This paper presents a two‐scale approximation of the Schur complement of a subdomain's stiffness matrix, obtained by combining local (i.e. element strips) and global (i.e. homogenized) contributions. This approximation is used in the context of a coupling strategy that is designed to embed local plasticity and geometric details into a small region of a large linear elastic structure; the strategy consists in creating a local model that contains the desired features of the concerned region and then substituting it into the global problem by the means of a non‐intrusive solver coupling technique adapted from domain decomposition methods. Using the two‐scale approximation of the Schur complement as a Robin condition on the local model enables to reach high efficiency. Examples include a large 3D problem provided by our industrial partner Snecma. Copyright © 2011 John Wiley & Sons, Ltd.