Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
470463 | Computers & Mathematics with Applications | 2014 | 7 Pages |
Abstract
Sobolev gradients have been discussed in Sial et al. (2003) as a method for energy minimization related to Ginzburg–Landau functionals. In this article, a weighted Sobolev gradient approach for the time evolution of a Ginzburg–Landau functional is presented for different values of κκ. A comparison is given between the weighted and unweighted Sobolev gradients in a finite element setting. It is seen that for small values of κκ, the weighted Sobolev gradient method becomes more and more efficient compared to using the unweighted Sobolev gradient. A comparison with Newton’s method is given where the failure of Newton’s method is demonstrated for a test problem.
Keywords
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Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Nauman Raza, Sultan Sial, Asma Rashid Butt,