4 papers
Nonlinear optimization in Hilbert space using Sobolev gradients with applications
Parimah Kazemi, Robert Renka
The problem of finding roots or solutions of a nonlinear partial differential equation may be formulated as the problem of minimizing a sum of squared residuals. One then defines a…
Sobolev gradients and image interpolation
Parimah Kazemi, Ionut Danaila
We present here a new image inpainting algorithm based on the Sobolev gradient method in conjunction with the Navier-Stokes model. The original model of Bertalmio et al is reformul…
A new Sobolev gradient method for direct minimization of the Gross-Pitaevskii energy with rotation
Ionut Danaila, Parimah Kazemi
In this paper we improve traditional steepest descent methods for the direct minimization of the Gross-Pitaevskii (GP) energy with rotation at two levels. We first define a new inn…
Tackling the Gross-Pitaevskii energy functional with the Sobolev gradient - Analytical and numerical results
P. Kazemi, M. Eckart
In the first part of this contribution we prove the global existence and uniqueness of a trajectory that globally converges to the minimizer of the Gross-Pitaevskii energy function…