Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Two-Level discretization techniques for ground state computations of Bose-Einstein condensates

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      This work presents a new methodology for computing ground states of Bose-Einstein condensates based on finite element discretizations on two different scales of numerical resolution. In a pre-processing step, a low-dimensional (coarse) generalized finite element space is constructed. It is based on a local orthogonal decomposition and exhibits high approximation properties. The non-linear eigenvalue problem that characterizes the ground state is solved by some suitable iterative solver exclusively in this low-dimensional space, without loss of accuracy when compared with the solution of the full fine scale problem. The pre-processing step is independent of the types and numbers of bosons. A post-processing step further improves the accuracy of the method. We present rigorous a priori error estimates that predict convergence rates H^3 for the ground state eigenfunction and H^4 for the corresponding eigenvalue without pre-asymptotic effects; H being the coarse scale discretization parameter. Numerical experiments indicate that these high rates may still be pessimistic.

      Related collections

      Author and article information

      Journal
      2013-05-17
      2014-05-20
      1305.4080

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

      Custom metadata
      35Q55, 65N15, 65N25, 65N30, 81Q05
      Accepted for publication in SIAM J. Numer. Anal., 2014
      math.NA

      Numerical & Computational mathematics

      Comments

      Comment on this article