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Two-level discretiz...
Two-level discretization techniques for ground state computations of Bose-Einstein condensates
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- Henning, Patrick (author)
- Ecole Polytechnique Federale de Lausanne (EPFL),Swiss Federal Institute of Technology in Lausanne (EPFL)
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- Målqvist, Axel, 1978 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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- Peterseim, Daniel (author)
- Universität Bonn,University of Bonn
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(creator_code:org_t)
- Society for Industrial & Applied Mathematics (SIAM), 2014
- 2014
- English.
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In: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 52:4, s. 1525-1550
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Abstract
Subject headings
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- 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 preprocessing step, a low-dimensional (coarse) generalized finite element space is constructed. It is based on a local orthogonal decomposition of the solution space and exhibits high approximation properties. The nonlinear eigenvalue problem that characterizes the ground state is solved by some suitable iterative solver exclusively in this low-dimensional space, without significant loss of accuracy when compared with the solution of the full fine scale problem. The preprocessing step is independent of the types and numbers of bosons. A postprocessing 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- eigenvalue
- finite element
- Gross-Pitaevskii equation
- numerical upscaling
- two-grid method
- multiscale method
- Gross-Pitaevskii equation
Publication and Content Type
- ref (subject category)
- art (subject category)
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