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math.NA2026
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…
math.NA2025
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…
math.NA2025
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…