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：本文提出了一种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、区域分解和模型降阶技术。通过引入位移场的可加性分裂，针对无明确尺度分离的应用场景，实现细观尺度对宏观尺度影响的建模。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，我们通过全局降阶问题为边界条件提供先验信息，并将采用物理意义相关样本的方法与现有采用非相关样本的方法进行对比。局部空间的设计使得各子域的局部贡献能够以协调方式耦合，同时保留标准有限元装配过程的稀疏模式。多组数值实验验证了该方法的精确性和高效性，并表明相较于非相关采样方法，该方法具有缩减局部空间规模和训练样本数量的潜力。