Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast hybrid numerical-asymptotic boundary element methods for high
  frequency screen and aperture problems based on least-squares collocation   We present a hybrid numerical-asymptotic (HNA) boundary element method (BEM)
for high frequency scattering by two-dimensional screens and apertures, whose
computational cost to achieve any prescribed accuracy remains bounded with
increasing frequency. Our method is a collocation implementation of the high
order hp HNA approximation space of Hewett et al. IMA J. Numer. Anal. 35
(2015), pp.1698- 1728, where a Galerkin implementation was studied.
  An advantage of the current collocation scheme is that the one-dimensional
highly oscillatory singular integrals appearing in the BEM matrix entries are
significantly easier to evaluate than the two-dimensional integrals appearing
in the Galerkin case, which leads to much faster computation times. Here we
compute the required integrals at frequency-independent cost using the
numerical method of steepest descent, which involves complex contour
deformation.
  The change from Galerkin to collocation is nontrivial because naive
collocation implementations based on square linear systems suffer from severe
numerical instabilities associated with the numerical redundancy of the HNA
basis, which produces highly ill-conditioned BEM matrices. In this paper we
show how these instabilities can be removed by oversampling, and solving the
resulting overdetermined collocation system in a weighted least-squares sense
using a truncated singular value decomposition. On the basis of our numerical
experiments, the amount of oversampling required to stabilise the method is
modest (around 25% typically suffices) and independent of frequency. As an
application of our method we present numerical results for high frequency
scattering by prefractal approximations to the middle-third Cantor set.

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The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an