In this work I present a constructive method for finding critical points of the Ginzburg-Landau energy functional using the method of Sobolev gradients. I give a description of the construction of the Sobolev gradient and obtain convergence results for continuous steepest descent with this gradient. I study the Ginzburg-Landau functional with magnetic field and the Ginzburg-Landau functional without magnetic field. I then present the numerical results I obtained by using steepest descent with the discretized Sobolev gradient.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc9075 |
| Date | 08 1900 |
| Creators | Kazemi, Parimah |
| Contributors | Neuberger, John W., Renka, Robert J., Betelu, Santiago |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Copyright, Kazemi, Parimah, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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