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# Arc-length Continuation and Multi-grid Techniques for Nonlinear Elliptic Eigenvalue Problems *

@inproceedings{TonyArclengthCA, title={Arc-length Continuation and Multi-grid Techniques for Nonlinear Elliptic Eigenvalue Problems *}, author={Tony and F. Ciccarese and Chan and H. Biessy and Keller} }

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… CONTINUE READING