Low-rank approximation for multiscale PDEs
Numerical Analysis
2022-03-09 v2 Numerical Analysis
Abstract
Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing multiscale problems through random sampling. This is achieved by incorporating randomized SVD solvers and manifold learning techniques to numerically reconstruct the low-rank features of multiscale PDEs. We use multiscale radiative transfer equation and elliptic equation with rough media to showcase the application of this framework.
Cite
@article{arxiv.2111.12904,
title = {Low-rank approximation for multiscale PDEs},
author = {Ke Chen and Shi Chen and Qin Li and Jianfeng Lu and Stephen J. Wright},
journal= {arXiv preprint arXiv:2111.12904},
year = {2022}
}