Arc-Length Continuation and Multigrid Techniques for Nonlinear Elliptic Eigenvalue Problems
- Creators
- Chan, Tony F. C.
- Keller, H. B.
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.
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.Files
| Name | Size | Download all |
|---|---|---|
|
md5:6f9d73e360304a3fa2a71239aa3a3db1
|
2.5 MB | Preview Download |
Additional details
- Eprint ID
- 9912
- Resolver ID
- CaltechAUTHORS:CHAsiamjssc82
- Created
-
2008-03-26Created from EPrint's datestamp field
- Updated
-
2021-11-08Created from EPrint's last_modified field