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2000•Journal of Computational PhysicsOpen access

Computational Harmonic Analysis for Tensor Fields on the Two-Sphere

Peter J. Kostelec, David K. Maslen, Dennis M. Healy, Daniel N. Rockmore

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Abstract

In this paper we describe algorithms for the numerical computation of Fourier transforms of tensor fields on the two-sphere, S 2 . These algorithms reduce the computation of an expansion on tensor spherical harmonics to expansions in scalar spherical harmonics, and hence can take advantage of recent improvements in the efficiency of computation of scalar spherical harmonic transforms.

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What this paper is about

In this paper we describe algorithms for the numerical computation of Fourier transforms of tensor fields on the two-sphere, S 2 . These algorithms reduce the computation of an expansion on tensor spherical harmonics to expansions in scalar spherical harmonics, and hence can take advantage of recent improvements in the efficiency of computation of scalar spherical harmonic transforms.

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Available abstract

In this paper we describe algorithms for the numerical computation of Fourier transforms of tensor fields on the two-sphere, S 2 . These algorithms reduce the computation of an expansion on tensor spherical harmonics to expansions in scalar spherical harmonics, and hence can take advantage of recent improvements in the efficiency of computation of scalar spherical harmonic transforms.

Key concepts: Spherical harmonics, Zonal spherical harmonics, Spin-weighted spherical harmonics, Solid harmonics, Tensor operator, Computation, Scalar (mathematics), Vector spherical harmonics

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