A finite element method with mesh adaptivity for computing vortex states in fast-rotating Bose-Einstein condensates

  • Authors:

  • Ionut Danaila;Frédéric Hecht

  • Affiliations:

  • UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France and CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France;UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France and CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

Numerical computations of stationary states of fast-rotating Bose-Einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices. In this paper we propose a low-order finite element method with mesh adaptivity by metric control, as an alternative approach to the commonly used high-order (finite difference or spectral) approximation methods. The mesh adaptivity is used with two different numerical algorithms to compute stationary vortex states: an imaginary time propagation method and a Sobolev gradient descent method. We first address the basic issue of the choice of the variable used to compute new metrics for the mesh adaptivity and show that refinement using simultaneously the real and imaginary part of the solution is successful. Mesh refinement using only the modulus of the solution as adaptivity variable fails for complicated test cases. Then we suggest an optimized algorithm for adapting the mesh during the evolution of the solution towards the equilibrium state. Considerable computational time saving is obtained compared to uniform mesh computations. The new method is applied to compute difficult cases relevant for physical experiments (large nonlinear interaction constant and high rotation rates).