Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the ground state and dynamics of the nonlinear Schr\"odinger
  equation with nonlocal interactions via the nonuniform FFT   We present efficient and accurate numerical methods for computing the ground
state and dynamics of the nonlinear Schr\"odinger equation (NLSE) with nonlocal
interactions based on a fast and accurate evaluation of the long-range
interactions via the nonuniform fast Fourier transform (NUFFT). We begin with a
review of the fast and accurate NUFFT based method in \cite{JGB} for nonlocal
interactions where the singularity of the Fourier symbol of the interaction
kernel at the origin can be canceled by switching to spherical or polar
coordinates. We then extend the method to compute other nonlocal interactions
whose Fourier symbols have stronger singularity at the origin that cannot be
canceled by the coordinate transform. Many of these interactions do not decay
at infinity in the physical space, which adds another layer of complexity since
it is more difficult to impose the correct artificial boundary conditions for
the truncated bounded computational domain. The performance of our method
against other existing methods is illustrated numerically, with particular
attention on the effect of the size of the computational domain in the physical
space. Finally, to study the ground state and dynamics of the NLSE, we propose
efficient and accurate numerical methods by combining the NUFFT method for
potential evaluation with the normalized gradient flow using backward Euler
Fourier pseudospectral discretization and time-splitting Fourier pseudospectral
method, respectively. Extensive numerical comparisons are carried out between
these methods and other existing methods for computing the ground state and
dynamics of the NLSE with various nonlocal interactions. Numerical results show
that our scheme performs much better than those existing methods in terms of
both accuracy and efficiency.

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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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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: hep-lat
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The categories of this paper are: alg-geom