论文标题
一个新的分析框架，用于不精确的两网格方法的收敛性
A new analytical framework for the convergence of inexact two-grid methods
论文作者
论文摘要
多格里德社区已经很好地研究了具有精确溶液的两网格方法：已经建立了优雅的身份，以表征精确的两网格方法的收敛因子。但是，在实践中，精确地解决Galerkin粗网格系统通常太昂贵了，尤其是当它的尺寸较大时。取而代之的是，如果没有必要的收敛速度损失，则可以大约解决粗网络系统。在本文中，我们开发了一个新的框架，用于分析不精确的两网格方法的收敛：介绍了误差传播矩阵的两侧界限，介绍了不精确的两个网格方法的误差。在框架中，使用精确的两个网格收敛的身份涉及的限制性更平滑，以测量实际的粗网格矩阵与Galerkin One偏离的距离。作为应用程序，我们为多族方法建立了统一的收敛理论。
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.
