A fast spherical harmonics transform algorithm

Authors:
Reiji Suda and Masayasu Takami

Journal:
Math. Comp. **71** (2002), 703-715

MSC (2000):
Primary 65T99, 42C10

DOI:
https://doi.org/10.1090/S0025-5718-01-01386-2

Published electronically:
November 28, 2001

MathSciNet review:
1885622

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Reiji Suda**

Affiliation:
Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan

Email:
reiji@na.cse.nagoya-u.ac.jp

**Masayasu Takami**

Affiliation:
Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan

Email:
m-takami@kubota.co.jp

DOI:
https://doi.org/10.1090/S0025-5718-01-01386-2

Keywords:
Spherical harmonics transform,
associated Legendre transform,
fast transform algorithm,
computational complexity

Received by editor(s):
January 24, 2000

Received by editor(s) in revised form:
July 10, 2000

Published electronically:
November 28, 2001

Additional Notes:
This research is partly supported by the Japan Society for Promotion of Science (Computational Science and Engineering for Global Scale Flow Systems Project), Grant-in-Aid #11450038 of the Ministry of Education, and the Toyota Physical and Chemical Research Institute.

Article copyright:
© Copyright 2001
American Mathematical Society