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A two-scale approximation of the Schur complement and its use for non-intrusive coupling

Abstract : This paper presents a two-scale approximation of the Schur complement of a subdomain's stiffness matrix, obtained by combining local (ie. element strips) and global (ie. 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 which 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.
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Submitted on : Thursday, June 11, 2020 - 1:01:12 PM
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Lionel Gendre, Olivier Allix, Pierre Gosselet. A two-scale approximation of the Schur complement and its use for non-intrusive coupling. International Journal for Numerical Methods in Engineering, Wiley, 2011, 87 (9), pp.889-905. ⟨10.1002/nme.3142⟩. ⟨hal-01224373⟩

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