Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Reduced Order Modeling technique to study bifurcating phenomena:
  application to the Gross-Pitaevskii equation   We propose a computationally efficient framework to treat nonlinear partial
differential equations having bifurcating solutions as one or more physical
control parameters are varied. Our focus is on steady bifurcations. Plotting a
bifurcation diagram entails computing multiple solutions of a parametrized,
nonlinear problem, which can be extremely expensive in terms of computational
time. In order to reduce these demanding computational costs, our approach
combines a continuation technique and Newton's method with a Reduced Order
Modeling (ROM) technique, suitably supplemented with a hyper-reduction method.
To demonstrate the effectiveness of our ROM approach, we trace the steady
solution branches of a nonlinear Schr\"{o}dinger equation, called
Gross-Pitaevskii equation, as one or two physical parameters are varied. In the
two parameter study, we show that our approach is 60 times faster in
constructing a bifurcation diagram than a standard Full Order Method.

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The categories of this paper are: eess
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys