4 papers · 1 filter
Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method
Yuhe Wang, Min Wang
Physics-governed models are increasingly paired with machine learning for accelerated predictions, yet most "physics--informed" formulations treat the governing equations as a pena…
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…
Implicit-Explicit Scheme with Multiscale Vanka Two-Grid Solver for Heterogeneous Unsaturated Poroelasticity
Maria Vasilyeva, Ben S. Southworth, Yunhui He +1
We consider a coupled nonlinear system of equations that describe unsaturated flow in heterogeneous poroelastic media. For the numerical solution, we use a finite element approxima…
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…