
arXiv: 2201.10374
AbstractIn this article, a methodology for fine scale modeling of large scale linear elastic structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse scale is modeled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed by solving an oversampling problem with random boundary conditions. Herein, we inform the boundary conditions by a global reduced problem and compare our approach using physically meaningful correlated samples with existing approaches using uncorrelated samples. The local spaces are designed such that the local contribution of each subdomain can be coupled in a conforming way, which also preserves the sparsity pattern of standard finite element assembly procedures. Several numerical experiments show the accuracy and efficiency of the method, as well as its potential to reduce the size of the local spaces and the number of training samples compared to the uncorrelated sampling.
localized model order reduction, FOS: Computer and information sciences, Multigrid methods; domain decomposition for boundary value problems involving PDEs, variational multiscale method, Finite element methods applied to problems in solid mechanics, Linear elasticity with initial stresses, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, domain decomposition methods, Computational Engineering, Finance, and Science (cs.CE), Variational methods applied to PDEs, multiscale methods, PDEs in connection with mechanics of deformable solids, Computer Science - Computational Engineering, Finance, and Science
localized model order reduction, FOS: Computer and information sciences, Multigrid methods; domain decomposition for boundary value problems involving PDEs, variational multiscale method, Finite element methods applied to problems in solid mechanics, Linear elasticity with initial stresses, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, domain decomposition methods, Computational Engineering, Finance, and Science (cs.CE), Variational methods applied to PDEs, multiscale methods, PDEs in connection with mechanics of deformable solids, Computer Science - Computational Engineering, Finance, and Science
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