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- W2963863319 endingPage "100013" @default.
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- W2963863319 abstract "This paper presents a method for accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The method 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 gradient and divergence. 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." @default.
- W2963863319 created "2019-07-30" @default.
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- W2963863319 date "2019-06-01" @default.
- W2963863319 modified "2023-10-01" @default.
- W2963863319 title "Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: Mathematical analysis and derivations" @default.
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- W2963863319 doi "https://doi.org/10.1016/j.jcpx.2019.100013" @default.
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