A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates
Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
Energy minimization using Sobolev gradients: application to phase separation and ordering
Journal of Computational Physics
Constructing fair curves and surfaces with a Sobolev gradient method
Computer Aided Geometric Design
Journal of Computational Physics
Energy minimization related to the nonlinear Schrödinger equation
Journal of Computational Physics
On the partial difference equations of mathematical physics
IBM Journal of Research and Development
Preconditioning operators and Sobolevgradients for nonlinear elliptic problems
Computers & Mathematics with Applications
Sobolev gradient preconditioning for the electrostatic potential equation
Computers & Mathematics with Applications
Journal of Computational Physics
Application of Sobolev gradient method to Poisson-Boltzmann system
Journal of Computational Physics
Approximate solutions to Poisson-Boltzmann systems with Sobolev gradients
Journal of Computational Physics
| Hi-index | 0.09 |
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 @k. A comparison is given between the weighted and unweighted Sobolev gradients in a finite element setting. It is seen that for small values of @k, 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.