Multi-scale domain decomposition method for large scale structural analysis with a zooming technique : Application to plate assembly

International audienceThis article is concerned with a multi-scale domain decomposition method (DDM), based on the FETI-DP solver, for large-scale structural elastic analysis and suited to problems that exhibit structural heterogeneities, such as plate assemblies in the presence of structural details. In this approach once a partition of the global fine mesh into subdomains has been performed (all subdomains possess a fine mesh) and to optimize the computational time, the fine mesh is preserved only in the zones of interest (with local phenomena due to discontinuity, hole, etc.) while the remaining subdomains are replaced by numerical homogenized coarse elements. Indeed, the multi-scale aspect is introduced by the description of subdomains with either a fine or a coarse scale mesh. As a result, an extension of the FETI-DP DDM is proposed in this article (called herein FETI-DP micro-macro) that allows the simultaneous usage of different discretizations: fine (microscopic) mesh for subdomains in zones of interest and coarse (macroscopic or homogenized) mesh for the complementary part of the structure. Using this strategy raises the problem of the determination of the stiffness of coarse subdomains, and of the incompatible finite element connection between fine and coarse subdomains. Two approaches (collocation and Mortar) are presented and compared. The article ends with patch tests and some numerical examples in 2D and 3D. The obtained numerical results exemplify the efficiency and capability of the FETI-DP micro-macro approach and reveal that the Mortar approach is more accurate, at constant cost, than the collocation approach