We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices and optimal reduced bases. A memory-efficient methodology is proposed to project the global finite element linear system onto the reduced basis. Our numerical results demonstrate the technique using non-trivial tetrahedral meshes and subdomain interfaces 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：本文针对云环境下椭圆型边值问题的分布式有限元求解，扩展了一种局部化模型降阶方法。我们提出了一种计算高效的技术，用于计算所需的内积矩阵和最优降阶基，并设计了一种内存高效的方法，将全局有限元线性系统投影到降阶基上。数值实验通过将模型降阶的主要计算任务分布到云端，在笔记本电脑上使用非平凡四面体网格和子域接口，处理了高达8500万自由度的算例，验证了该技术的有效性。