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Arc-Length Continuation and Multigrid Techniques for Nonlinear Elliptic Eigenvalue Problems

Chan, Tony F. C. and Keller, H. B. (1982) Arc-Length Continuation and Multigrid Techniques for Nonlinear Elliptic Eigenvalue Problems. SIAM Journal on Scientific and Statistical Computing, 3 (2). pp. 173-194. ISSN 0196-5204. http://resolver.caltech.edu/CaltechAUTHORS:CHAsiamjssc82

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Abstract

We investigate multi-grid methods for solving linear systems arising from arc-length continuation techniques applied to nonlinear elliptic eigenvalue problems. We find that the usual multi-grid methods diverge in the neighborhood of singular points of the solution branches. As a result, the continuation method is unable to continue past a limit point in the Bratu problem. This divergence is analyzed and a modified multi-grid algorithm has been devised based on this analysis. In principle, this new multi-grid algorithm converges for elliptic systems, arbitrarily close to singularity and has been used successfully in conjunction with arc-length continuation procedures on the model problem. In the worst situation, both the storage and the computational work are only about a factor of two more than the unmodified multi-grid methods.


Item Type:Article
Additional Information:©1982 Society for Industrial and Applied Mathematics. Received by the editors April 1, 1981. This author’s [T.F.C.C.] work was supported by the U.S. Department of Energy under contract EY-76-S-03-070 while he was at California Institute of Technology and by the Office of Naval Research under grant N00014-80-0076 under subcontract from Florida State University while he was at Yale. This author’s [H.B.K.] work was supported by the U.S. Department of Energy under contract EY-76-S-03-070 and by the U.S. Army Research Office under contract DAAG 29-78-C-0011.
Subject Keywords:multi-grid; arc-length continuation; nonlinear elliptic eigenvalue problems; singular systems
Record Number:CaltechAUTHORS:CHAsiamjssc82
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CHAsiamjssc82
Alternative URL:http://dx.doi.org/10.1137/0903012
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9912
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:26 Mar 2008
Last Modified:26 Dec 2012 09:54

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