We study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross–Pitaevskii equation. In particular, we explore its capability of preserving a steady-state vortex solution, whose density profile is approximated by an accurate diagonal Padé expansion of degree [8,8], here explicitly derived for the first time. We show by several numerical experiments that the Fourier spectral method is only slightly more accurate than a time splitting finite difference scheme, while being reliable and efficient. Moreover, we notice that, at a post-processing stage, it allows an accurate evaluation of the solution outside grid points, thus becoming particularly appealing for applications where high resolution is needed, such as in the study of quantum vortex interactions.

Reliability of the time splitting Fourier method for singular solutions in quantum fluids

Caliari, M.
;
Zuccher, S.
2018-01-01

Abstract

We study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross–Pitaevskii equation. In particular, we explore its capability of preserving a steady-state vortex solution, whose density profile is approximated by an accurate diagonal Padé expansion of degree [8,8], here explicitly derived for the first time. We show by several numerical experiments that the Fourier spectral method is only slightly more accurate than a time splitting finite difference scheme, while being reliable and efficient. Moreover, we notice that, at a post-processing stage, it allows an accurate evaluation of the solution outside grid points, thus becoming particularly appealing for applications where high resolution is needed, such as in the study of quantum vortex interactions.
2018
Fourier spectral method, Gross-Pitaevskii equation, nonlinear Schroedinger equation, nonuniform finite differences, quantum fluids, time splitting
File in questo prodotto:
File Dimensione Formato  
CZ16.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Documento in Pre-print
Licenza: Dominio pubblico
Dimensione 576.99 kB
Formato Adobe PDF
576.99 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/973170
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 10
social impact