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arXiv · 2609.09911

The geometric convergence of a parallel domain decomposition method on manifolds

Lizhen Qin
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Abstract

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.

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Lizhen Qin. 2026-09-09. The geometric convergence of a parallel domain decomposition method on manifolds. https://arxiv.org/abs/2609.09911

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