4 papers
I-MCHM: Interface Multicontinuum Homogenization for Multiscale Elliptic Problems
Wing Tat Leung, Zhihang Xu
We introduce an interface multicontinuum homogenization method (I-MCHM) for high-contrast elliptic problems whose subdomains may have distinct microscopic patterns and unequal numb…
Parametrization of subgrid scales in long-term simulations of the shallow-water equations using machine learning and convex limiting
Md Amran Hossan Mojamder, Zhihang Xu, Min Wang +1
We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network…
Numerical Methods for Solving Nonlinearly Coupled Poisson Equations in Dual-Continuum Modeled Porous Electrodes
Yuhe Wang, Min Wang, Zhihang Xu
Porous electrodes are widely used in electrochemical systems, where accurately determining electric potentials, particularly overpotentials, is essential for understanding electrod…
Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs
Zhihang Xu, Min Wang, Zhu Wang
While deep learning has achieved remarkable success in solving partial differential equations (PDEs), it still faces significant challenges, particularly when the PDE solutions hav…