Schwarz iteration method for elliptic equation with rough media based on random sampling

Abstract

We propose a computationally efficient Schwarz method for elliptic equations with rough media. A random sampling strategy is used to find low-rank approximations of all local solution maps in the offline stage; these maps are used to perform fast Schwarz iterations in the online stage. Numerical examples demonstrate accuracy and robustness of our approach.

References in corpus (1)

• Random Sampling and Efficient Algorithms for Multiscale PDEs

Cited by in corpus (1)

• A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks