Publication Type
Journal
Journal Name
ACM Transactions on Mathematical Software
Publication Date
Page Number
23
Volume
35
Issue
3
Abstract
A collection of MATLAB classes for computing spherical harmonic transforms
are presented and used to solve simple partial differential equations
on the sphere.
The spectral synthesis and analysis using fast Fourier transforms and Legendre
transforms with the associated Legendre functions are presented in depth.
A set of methods associated with a spectral\_field class provides spectral
approximation to the $\DIV$, $\CURL$, $\GRAD$, and $\LAPL$ in spherical geometr
y.
Laplace inversion and Helmholtz equation solvers are also methods for this clas
s.
Investigation of algorithms and analysis for spherical harmonic transform optio
ns
for parallel high performance computers are discussed in the context of global
climate
and weather models.