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arXiv · 2204.07918

Convergence analysis of two-grid methods for nonsymmetric positive definite systems

Xuefeng Xu
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Abstract

The convergence theory of multigrid methods for symmetric positive definite systems is well established. For nonsymmetric systems, however, the corresponding theory remains far from mature. Two-grid analysis is fundamental to the design and analysis of multigrid methods. This paper presents a convergence analysis of two-grid methods for nonsymmetric positive definite systems. When the coarse-grid system is solved exactly, we derive a succinct identity for the two-grid convergence factor measured in a smoother-induced norm. More generally, under mild assumptions, we develop a convergence theory for inexact two-grid methods, where convergence is measured in a generic norm.

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Xuefeng Xu. 2022-04-17. Convergence analysis of two-grid methods for nonsymmetric positive definite systems. https://arxiv.org/abs/2204.07918

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