Lizhen Qin, Feng Wang, Yun Wang
Published 2024-02-01, updated 2025-01-13Version 2
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 need for global triangulations or grids on the manifolds. Additionally, it features a highly parallel iterative scheme. To verify its efficacy, we conduct numerical experiments on some $4$-dimensional manifolds without and with boundary.
Comments: Final version. To appear in SIAM Journal on Scientific Computing
A numerical domain decomposition method for solving elliptic equations on manifolds
Strictly positive definite kernels on compact Riemannian manifolds
Numerical calculation method for function integration on submanifolds of $\mathbb{R}^n$ or compact Riemannian manifolds
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