A fast spherical harmonics transform algorithm |
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Authors: | Reiji Suda Masayasu Takami |
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Institution: | Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan ; Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan |
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Abstract: | The spectral method with discrete spherical harmonics transform plays an important role in many applications. In spite of its advantages, the spherical harmonics transform has a drawback of high computational complexity, which is determined by that of the associated Legendre transform, and the direct computation requires time of for cut-off frequency . In this paper, we propose a fast approximate algorithm for the associated Legendre transform. Our algorithm evaluates the transform by means of polynomial interpolation accelerated by the Fast Multipole Method (FMM). The divide-and-conquer approach with split Legendre functions gives computational complexity . Experimental results show that our algorithm is stable and is faster than the direct computation for . |
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Keywords: | Spherical harmonics transform associated Legendre transform fast transform algorithm computational complexity |
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