We present a method for the distributed finite element solution of elliptic boundary value problems using model order reduction on each subdomain of the domain decomposition. We show that the error of the reduction can be succesfully controlled in the $H^1$ norm due to the properly weighted $l^2$ low-rank approximation. Our numerical results demonstrate the technique using tetrahedral meshes with up to 85 million degrees-of-freedom on a laptop computer by distributing the bulk of the model order reduction to the cloud.

翻译：本文提出了一种利用模型降阶方法求解椭圆型边值问题的分布式有限元方法，该方法在每个子域上执行域分解。研究表明，通过适当加权的$l^2$低秩逼近，可在$H^1$范数下有效控制降阶误差。数值实验表明，通过将模型降阶的主体计算分布于云端，该技术可在笔记本电脑上处理包含高达8500万自由度的四面体网格。