On the nonlinear domain decomposition method
type: Item
instance of: scholarly article
title: On the nonlinear domain decomposition method
zbMATH Open document ID: 0891.65126
DOI: 10.1007/BF02510214
published in: BIT
publication date: 1998-07-19T00:00:00Z
review text: The known abstract framework of the subspace iteration method for linear problems is generalized to the nonlinear case. The proposed method requires the solution of local nonlinear problems and a global problem. The presented analysis shows (under relatively weak assumptions) that the nonlinear iteration converges locally at the same asymptotic rate as the corresponding linear iteration applied to the linearized problem. The analysis is similar to the technique developed in the multigrid method for nonlinear problems. Next, conditions which guarantee the global convergence of the method are discussed. It should be noted that the proposed algorithm uses different strategies depending on whether the iterates are in a neighbourhood of the solution or outside.
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1033761
zbMATH Keywords: nonlinear domain decomposition method
zbMATH Keywords: subspace iteration method
zbMATH Keywords: multigrid method
zbMATH Keywords: global convergence
zbMATH Keywords: algorithm
author: Maksymilian Dryja
author: Wolfgang Hackbusch
reviewed by: Raytcho D. Lazarov
MaRDI profile type: Publication
cites work: Q4326654
cites work: Multiplicative Schwarz Algorithms for Some Nonsymmetric and Indefinite Problems
cites work: Q4162607
cites work: Domain Decomposition Algorithms with Small Overlap
cites work: Q3727300
cites work: Iterative solution of large sparse systems of equations. Transl. from the German
cites work: Analysis of a damped nonlinear multilevel method
description: scientific article; zbMATH DE number 1033761