Manifold Learning and Nonlinear Homogenization
arxiv(2021)
摘要
We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tangent spaces spanned by the nearest neighbors to compress local solution manifolds. Our framework is applied to a semilinear elliptic equation with oscillatory media and a nonlinear radiative transfer equation; in both cases, significant improvements in efficacy are observed. This new method does not rely on detailed analytical understanding of the multiscale PDEs, such as their asymptotic limits, and thus is more versatile for general multiscale problems.
更多查看译文
关键词
Key words,nonlinear homogenization,multiscale problems,manifold learning,domain decomposition
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络