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:本文提出了大规模结构的微幅模型方法,该方法结合了多尺度的变式方法、域分解和示范订单的减少。微幅对粗糙规模的影响,通过使用迁移场的添加式分割模型进行模拟,处理没有明确尺度分离的应用。局部缩小的空间是通过解决随机边界条件的过度抽样问题来建造的。这里,我们用全球减少的问题来通报边界条件,并将我们使用具有实际意义的关联样品的方法与使用与非相关样品的现有方法进行比较。当地空间的设计使每个子域的局部贡献能够以一致的方式结合起来,这也保留标准有限元素组装程序的宽度模式。若干数字实验显示了该方法的准确性和效率,以及其缩小当地空间规模和训练样品数量的潜力,与与不相关的取样相比。