Parallel Algorithms for the Spectral Transform Method
SIAM Journal on Scientific Computing
Fast Shallow-Water equation solvers in latitude-longitude coordinates
Journal of Computational Physics
Journal of Computational Physics
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Spectral methods in MatLab
Generalized discrete spherical harmonic transforms
Journal of Computational Physics
A performance comparison of associated Legendre projections
Journal of Computational Physics
On the Efficient Parallel Computation of Legendre Transforms
SIAM Journal on Scientific Computing
A fast spherical harmonics transform algorithm
Mathematics of Computation
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
A semi-Lagrangian double Fourier method for the shallow water equations on the sphere
Journal of Computational Physics
Overview of the Software Design of the Community Climate System Model
International Journal of High Performance Computing Applications
Performance Portability in the Physical Parameterizations of the Community Atmospheric Model
International Journal of High Performance Computing Applications
Design and Implementation of Components in the Earth System Modeling Framework
International Journal of High Performance Computing Applications
Fast Algorithms for Spherical Harmonic Expansions
SIAM Journal on Scientific Computing
Spatiospectral Concentration on a Sphere
SIAM Review
Asymptotically fast algorithms for spherical and related transforms
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
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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.