Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation
نویسندگان
چکیده
We present an effective adaptive procedure for the numerical approximation of steady-state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and consists a combination novel finite element mesh refinement technique, which does not rely any posteriori error estimates, recently proposed new gradient flow. Numerical tests show that this strategy able to provide highly accurate results, with optimal convergence rates respect number degrees freedom.
منابع مشابه
A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the f...
متن کاملVortex helices for the Gross-Pitaevskii equation
We prove the existence of travelling vortex helices to the Gross-Pitaevskii equation in R. These solutions have an infinite energy, are periodic in the direction of the axis of the helix and have a degree one at infinity in the orthogonal direction. Résumé : Nous prouvons l’existence d’ondes progressives à vorticité sur une hélice pour l’équation de GrossPitaevskii dans R. Ces solutions sont d’...
متن کاملScattering for the Gross-Pitaevskii equation
We investigate the asymptotic behavior at time infinity of solutions close to a nonzero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau-Schrödinger) equation. We prove that, in dimensions larger than 3, small perturbations can be approximated at time infinity by the linearized evolution, and the wave operators are homeomorphic around 0 in certain Sobolev spaces.
متن کاملHaus/Gross-Pitaevskii equation for random lasers
Marco Leonetti, and Claudio Conti, 1 Dep. of Physics, University “Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy 2 CNR-ISC Institute for Complex Systems Dep. of Physics, University “Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy and ∗Corresponding author: [email protected], current address: Photonic Crystal Group, ICMM,C.Sor Juana Ins de la Cruz, 3, Cantoblanco, 28049 Madrid, Spain.
متن کاملRigorous derivation of the Gross-Pitaevskii equation.
The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2021
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2021.110165