Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor calculus in spherical coordinates using Jacobi polynomials.
  Part-I: Mathematical analysis and derivations   This paper presents a method for the accurate and efficient computations on
scalar, vector and tensor fields in three-dimensional spherical polar
coordinates. The methods uses spin-weighted spherical harmonics in the angular
directions and rescaled Jacobi polynomials in the radial direction. For the
2-sphere, spin-weighted harmonics allow for automating calculations in a
fashion as similar to Fourier series as possible. Derivative operators act as
wavenumber multiplication on a set of spectral coefficients. After transforming
the angular directions, a set of orthogonal tensor rotations put the radially
dependent spectral coefficients into individual spaces each obeying a
particular regularity condition at the origin. These regularity spaces have
remarkably simple properties under standard vector-calculus operations, such as
\textit{grad} and \textit{div}. We use a hierarchy of rescaled Jacobi
polynomials for a basis on these regularity spaces. It is possible to select
the Jacobi-polynomial parameters such that all relevant operators act in a
minimally banded way. Altogether, the geometric structure allows for the
accurate and efficient solution of general partial differential equations in
the unit ball.

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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga