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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.NA2024
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…
math.NA2022
A numerical domain decomposition method for solving elliptic equations on manifolds
Shuhao Cao, Lizhen Qin
A new numerical domain decomposition method is proposed for solving elliptic equations on compact Riemannian manifolds. The advantage of this method is to avoid global triangulatio…