In this paper, a methodology for fine scale modeling of large scale 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 modelled 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.

翻译：本文提出一种适用于大规模结构精细尺度建模的方法，该方法融合了变分多尺度方法、区域分解与模型降阶技术。通过位移场的加性分解技术对粗尺度中细尺度的影响进行建模，适用于无明确尺度分离的工程场景。通过求解具有随机边界条件的超采样问题构建局部降阶空间。在此过程中，我们采用全局降阶问题来定义边界条件，并将本方法使用的物理意义相关样本与现有方法中的非相关样本进行对比。局部空间的设计确保各子域局部贡献能以协调方式耦合，同时保持标准有限元装配程序的稀疏性模式。多项数值实验验证了该方法相较于非相关采样方法在保证精度与效率的同时，能有效缩减局部空间规模与训练样本数量。