3 papers
math.NA2026
Domain decomposition methods with Physics-informed neural networks for elliptic equations on manifolds
Yufang Jiang, Lizhen Qin, Feng Wang
We propose two numerical domain decomposition methods (DDMs) for elliptic equations on compact Riemannian manifolds, based on physics-informed neural networks (PINNs). Our approach…
math.GT2025
Self-covering, finiteness, commutativity, and fibering over tori
Lizhen Qin, Yang Su
A topological space is called self-covering if it is a nontrivial cover of itself. We prove that, under mild assumptions, a closed self-covering manifold with an abelian fundamenta…
math.NA2025
A parallel domain decomposition method for solving elliptic equations on manifolds
Lizhen Qin, Feng Wang, Yun Wang
We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the nee…