Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An extended Filon--Clenshaw--Curtis method for high-frequency wave
  scattering problems in two dimensions   We study the efficient approximation of integrals involving Hankel functions
of the first kind which arise in wave scattering problems on straight or convex
polygonal boundaries. Filon methods have proved to be an effective way to
approximate many types of highly oscillatory integrals, however finding such
methods for integrals that involve non-linear oscillators and
frequency-dependent singularities is subject to a significant amount of ongoing
research. In this work, we demonstrate how Filon methods can be constructed for
a class of integrals involving a Hankel function of the first kind. These
methods allow the numerical approximation of the integral at uniform cost even
when the frequency $\omega$ is large. In constructing these Filon methods we
also provide a stable algorithm for computing the Chebyshev moments of the
integral based on duality to spectral methods applied to a version of Bessel's
equation. Our design for this algorithm has significant potential for further
generalisations that would allow Filon methods to be constructed for a wide
range of integrals involving special functions. These new extended Filon
methods combine many favourable properties, including robustness in regard to
the regularity of the integrand and fast approximation for large frequencies.
As a consequence, they are of specific relevance to applications in wave
scattering, and we show how they may be used in practice to assemble
collocation matrices for wavelet-based collocation methods and for hybrid
oscillatory approximation spaces in high-frequency wave scattering problems on
convex polygonal shapes.

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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci