Publications [#367647] of Jianfeng Lu

Papers Published

1. Chen, S; Li, Q; Lu, J; Wright, SJ, MANIFOLD LEARNING AND NONLINEAR HOMOGENIZATION, Multiscale Modeling and Simulation, vol. 20 no. 3 (January, 2022), pp. 1093-1126 [doi]
   (last updated on 2026/01/15)

   Abstract:
   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 a detailed analytical understanding of multiscale PDEs, such as their asymptotic limits, and thus is more versatile for general multiscale problems.