论文标题
线性弹性异质结构通过局部模型降低的多尺度建模
Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction
论文作者
论文摘要
在本文中，提出了一种大规模建模的方法，该方法结合了变异多尺度方法，域分解和模型顺序减少。精细量表对粗尺度的影响是通过使用位移场的添加拆分来建模的，从而无需清晰的尺度分离来解决应用程序。通过解决随机边界条件的过采样问题来构建局部缩小空间。本文中，我们通过全局减少的问题告知边界条件，并使用物理有意义的相关样本与使用不相关样本的现有方法比较我们的方法。局部空间的设计使得每个子域的局部贡献都可以符合方式耦合，从而保留了标准有限元组装程序的稀疏模式。几个数值实验显示了该方法的准确性和效率，以及与不相关采样相比，其减少局部空间大小和训练样品数量的潜力。
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.
