A New Analytical Framework for the Convergence of Inexact Two-Grid Methods
A New Analytical Framework for the Convergence of Inexact Two-Grid Methods
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DOI：
10.1137/21m140448x
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发表时间：
2020-07
期刊：
影响因子：
--
通讯作者：
Xuefeng Xu;Chensong Zhang
中科院分区：
文献类型：
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作者：
Xuefeng Xu;Chensong Zhang
Two-grid methods with exact solution of the Galerkin coarse-grid system have been well studied by the multigrid community: an elegant identity has been established to characterize the convergence factor of exact two-grid methods. In practice, however, it is often too costly to solve the Galerkin coarse-grid system exactly, especially when its size is large. Instead, without essential loss of convergence speed, one may solve the coarse-grid system approximately. In this paper, we develop a new framework for analyzing the convergence of inexact two-grid methods: two-sided bounds for the energy norm of the error propagation matrix of inexact two-grid methods are presented. In the framework, a restricted smoother involved in the identity for exact two-grid convergence is used to measure how far the actual coarse-grid matrix deviates from the Galerkin one. As an application, we establish a unified convergence theory for multigrid methods.
