PreprintarXiv licencearXiv
The geometric convergence of a parallel domain decomposition method on manifolds
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.
Related
- Algebraic convergence analysis for the Interface Control Domain Decomposition (ICDD) method
- Curvature characterization of Hermitian manifolds with Bismut parallel torsion
- Pluriclosed manifolds with parallel Bismut torsion
- Fedosov manifolds with parallel symplectic Weyl curvature
- Compact lcK manifolds with Gauduchon parallel vector fields
BibTeX
@misc{qin2026geometric,
title = {{The geometric convergence of a parallel domain decomposition method on manifolds}},
author = {Lizhen Qin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09911},
eprint = {2609.09911},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09911},
}
RIS
TY - UNPB
TI - The geometric convergence of a parallel domain decomposition method on manifolds
AU - Lizhen Qin
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09911
UR - https://arxiv.org/abs/2609.09911
AB - 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.
ER -