A new characterization of the convergence factor of two-level methods

Xuefeng Xu

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arXiv · 2102.08600

A new characterization of the convergence factor of two-level methods

Xuefeng Xu

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Abstract

Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis and design of multilevel methods. In this paper, we present a concise and easy-to-use identity for characterizing the convergence factor of two-level methods, whose hierarchical spaces can be either overlapping or non-overlapping. In order to illustrate its usability and convenience, we give several applications, which offer new insights into the design of multilevel methods.

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Xuefeng Xu. 2021-02-17. A new characterization of the convergence factor of two-level methods. https://arxiv.org/abs/2102.08600

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