流形上并行区域分解方法的几何收敛性
The geometric convergence of a parallel domain decomposition method on manifolds
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中文总结 AI 辅助
本文证明了流形上椭圆方程连续区域分解方法的几何收敛性，并提供了收敛速率的多种估计，解决了该方法的收敛是否为几何收敛的开放问题。
中文摘要 AI 辅助
本文为流形上椭圆方程的连续区域分解方法建立了收敛理论。该方法起源于欧几里得域中的\cite{lions2}，后由\cite{qin_wang_wang}改编并推广到流形上。尽管其收敛性已知，但收敛是否为几何收敛仍悬而未决。我们证明了其几何收敛性，并给出了收敛速率的各种估计。
英文摘要
This paper establishes a convergence theory for a continuous domain decomposition method for elliptic equations on manifolds. This method originated in \cite{lions2} in the setting of Euclidean domains and was later adapted and generalized to manifolds by \cite{qin_wang_wang}. Although its convergence was known, whether the convergence is geometric has remained open. We prove its geometric convergence and provide various estimates on the convergence rate.
发表机构
- School of Mathematics, Nanjing University（南京大学数学系）
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