Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem:
  global convergence and computational efficiency   We propose a new normalized Sobolev gradient flow for the Gross-Pitaevskii
eigenvalue problem based on an energy inner product that depends on time
through the density of the flow itself. The gradient flow is well-defined and
converges to an eigenfunction. For ground states we can quantify the
convergence speed as exponentially fast where the rate depends on spectral gaps
of a linearized operator. The forward Euler time discretization of the flow
yields a numerical method which generalizes the inverse iteration for the
nonlinear eigenvalue problem. For sufficiently small time steps, the method
reduces the energy in every step and converges globally in $H^1$ to an
eigenfunction. In particular, for any nonnegative starting value, the ground
state is obtained. A series of numerical experiments demonstrates the
computational efficiency of the method and its competitiveness with established
discretizations arising from other gradient flows for this problem.

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The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th