Robust subspace correction methods for nearly singular systems

Young Ju Lee, Jinbiao Wu, Jinchao Xu, Ludmil Zikatanov

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

In this paper, we discuss convergence results for general (successive) subspace correction methods for solving nearly singular systems of equations. We provide parameter independent estimates under appropriate assumptions on the subspace solvers and space decompositions. The main assumption is that any component in the kernel of the singular part of the system can be decomposed into a sum of local (in each subspace) kernel components. This assumption also covers the case of "hidden" nearly singular behavior due to decreasing mesh size in the systems resulting from finite element discretizations of second order elliptic problems. To illustrate our abstract convergence framework, we analyze a multilevel method for the Neumann problem (H(grad) system), and also two-level methods for H(div) and H(curl) systems.

Original languageEnglish (US)
Pages (from-to)1937-1963
Number of pages27
JournalMathematical Models and Methods in Applied Sciences
Volume17
Issue number11
DOIs
StatePublished - Nov 2007

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

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