Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ARPIST: Provably Accurate and Stable Numerical Integration over
  Spherical Triangles   Abstract Numerical integration on spheres, including the computation of the
areas of spherical triangles, is a core computation in geomathematics. The
commonly used techniques sometimes suffer from instabilities and significant
loss of accuracy. We describe a new algorithm, called ARPIST, for accurate and
stable integration of functions on spherical triangles. ARPIST is based on an
easy-to-implement transformation to the spherical triangle from its
corresponding linear triangle via radial projection to achieve high accuracy
and efficiency. More importantly, ARPIST overcomes potential instabilities in
computing the Jacobian of the transformation, even for poorly shaped triangles
that may occur at poles in regular longitude-latitude meshes, by avoiding
potential catastrophic rounding errors. We compare our proposed technique with
L'Huilier's Theorem for computing the area of spherical triangles, and also
compare it with the recently developed LSQST method (J. Beckmann, H.N. Mhaskar,
and J. Prestin, GEM - Int. J. Geomath., 5:143-162, 2014) and a
radial-basis-function-based technique (J. A. Reeger and B. Fornberg, Stud.
Appl. Math., 137:174-188, 2015) for integration of smooth functions on
spherical triangulations. Our results show that ARPIST enables superior
accuracy and stability over previous methods while being orders of magnitude
faster and significantly easier to implement.

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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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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: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-ph