A Multilevel Nonlinear Method

A multilevel nonlinear method (MNM) for the numerical solution of nonlinear partial differential equations is developed. The MNM algorithm is motivated and analyzed using a simplified model which retains the essential features of the new approach. It is thereby shown to combine the advantages of the...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2006-01, Vol.28 (1), p.24-46
Main Authors: Yavneh, Irad, Dardyk, Gregory
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Iterative methods
Mathematical functions
Methods
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Summary:A multilevel nonlinear method (MNM) for the numerical solution of nonlinear partial differential equations is developed. The MNM algorithm is motivated and analyzed using a simplified model which retains the essential features of the new approach. It is thereby shown to combine the advantages of the two classical multigrid approaches to nonlinear problems. The analysis is supported by numerical tests for nonlinear differential equations in one and two dimensions.
ISSN:1064-8275
1095-7197
DOI:10.1137/040613809