Spherical Harmonic Transform Algorithms

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.