research-article

Algorithm 888: Spherical Harmonic Transform Algorithms

Authors:

Eduardo D’AzevedoAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 35, Issue 3

Article No.: 23, Pages 1 - 23

https://doi.org/10.1145/1391989.1404581

Published: 01 October 2008 Publication History

Abstract

A collection of MATLAB classes for computing and using spherical harmonic transforms is presented. Methods of these classes compute differential operators on the sphere and are used to solve simple partial differential equations in a spherical geometry. The spectral synthesis and analysis algorithms using fast Fourier transforms and Legendre transforms with the associated Legendre functions are presented in detail. A set of methods associated with a spectral_field class provides spectral approximation to the differential operators ∇ ⋯, ∇ ×, ∇, and ∇² in spherical geometry. Laplace inversion and Helmholtz equation solvers are also methods for this class. The use of the class and methods in MATLAB is demonstrated by the solution of the barotropic vorticity equation on the sphere. A survey of alternative algorithms is given and implementations for parallel high performance computers are discussed in the context of global climate and weather models.

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References

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Cited By

Marques RBouville CBouatouch K(2022)Gaussian Process for Radiance Functions on the SphereComputer Graphics Forum10.1111/cgf.1450141:6(67-81)Online publication date: 5-Apr-2022
https://doi.org/10.1111/cgf.14501
Chow YHan FZou J(2022)A direct sampling method for simultaneously recovering electromagnetic inhomogeneous inclusions of different natureJournal of Computational Physics10.1016/j.jcp.2022.111584(111584)Online publication date: Sep-2022
https://doi.org/10.1016/j.jcp.2022.111584
et al. O(2021)Analysis of Gegenbauer kernel filtration on the hypersphereInternational Journal of ADVANCED AND APPLIED SCIENCES10.21833/ijaas.2021.11.0018:11(1-9)Online publication date: Nov-2021
https://doi.org/10.21833/ijaas.2021.11.001
Show More Cited By

Index Terms

Algorithm 888: Spherical Harmonic Transform Algorithms
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations
    2. Numerical analysis
      1. Computation of transforms
  2. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 35, Issue 3

October 2008

164 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1391989

Issue’s Table of Contents

Copyright © 2008 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 October 2008

Accepted: 01 April 2008

Revised: 01 December 2007

Received: 01 October 2006

Published in TOMS Volume 35, Issue 3

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Cited By

Marques RBouville CBouatouch K(2022)Gaussian Process for Radiance Functions on the SphereComputer Graphics Forum10.1111/cgf.1450141:6(67-81)Online publication date: 5-Apr-2022
https://doi.org/10.1111/cgf.14501
Chow YHan FZou J(2022)A direct sampling method for simultaneously recovering electromagnetic inhomogeneous inclusions of different natureJournal of Computational Physics10.1016/j.jcp.2022.111584(111584)Online publication date: Sep-2022
https://doi.org/10.1016/j.jcp.2022.111584
et al. O(2021)Analysis of Gegenbauer kernel filtration on the hypersphereInternational Journal of ADVANCED AND APPLIED SCIENCES10.21833/ijaas.2021.11.0018:11(1-9)Online publication date: Nov-2021
https://doi.org/10.21833/ijaas.2021.11.001
Le Gia QLi MWang Y(2021)Algorithm 1018: FaVeST—Fast Vector Spherical Harmonic TransformsACM Transactions on Mathematical Software10.1145/345847047:4(1-24)Online publication date: 28-Sep-2021
https://dl.acm.org/doi/10.1145/3458470
Sohn SSakajo TKim S(2018)Stability of barotropic vortex strip on a rotating sphereProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences10.1098/rspa.2017.0883474:2210(20170883)Online publication date: 28-Feb-2018
https://doi.org/10.1098/rspa.2017.0883
Gimbutas ZGreengard L(2015)Computational Software: Simple FMM Libraries for Electrostatics, Slow Viscous Flow, and Frequency-Domain Wave PropagationCommunications in Computational Physics10.4208/cicp.150215.260615sw18:2(516-528)Online publication date: 30-Jul-2015
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