5 papers
Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation
Quentin Chauleur, Gaspard Kemlin
We prove the convergence in Zhidkov spaces of the first-order Lie-Trotter and the second-order Strang splitting schemes for the time integration of the Gross-Pitaesvkii equation wi…
Eigenvector-based acceleration strategies for gradient-type methods
Jean-Paul Chehab, Gaspard Kemlin, Marcos Raydan +1
Several strategies are described and analyzed to speed-up gradient-type methods when applied to the minimization of strictly convex quadratics and strictly convex functions. The pr…
Simulation of the magnetic Ginzburg-Landau equation via vortex tracking
Thiago Carvalho Corso, Gaspard Kemlin, Christof Melcher +1
This paper deals with the numerical simulation of the 2D magnetic time-dependent Ginzburg-Landau (TDGL) equations in the regime of small but finite (inverse) Ginzburg-Landau parame…
Fully guaranteed and computable error bounds on the energy for periodic Kohn-Sham equations with convex density functionals
Andrea Bordignon, Geneviève Dusson, Ãric Cancès +3
In this article, we derive fully guaranteed error bounds for the energy of convex nonlinear mean-field models. These results apply in particular to Kohn-Sham equations with convex…
Numerical simulation of the Gross-Pitaevskii equation via vortex tracking
Thiago Carvalho Corso, Gaspard Kemlin, Christof Melcher +1
This paper deals with the numerical simulation of the Gross-Pitaevskii (GP) equation, for which a well-known feature is the appearance of quantized vortices with core size of the o…