Fast algorithms for spherical harmonic expansions, II
Journal of Computational Physics
Algorithm 888: Spherical Harmonic Transform Algorithms
ACM Transactions on Mathematical Software (TOMS)
Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
ACM Transactions on Mathematical Software (TOMS)
Fast discrete algorithms for sparse Fourier expansions of high dimensional functions
Journal of Complexity
Journal of Computational and Applied Mathematics
Artificial Boundary Conditions for the Simulation of the Heat Equation in an Infinite Domain
SIAM Journal on Scientific Computing
Preparing scientific application software for exascale computing
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Hermitian Compact Interpolation on the Cubed-Sphere Grid
Journal of Scientific Computing
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An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere $S^2$ in ${\mathbb R}^3$ of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform), and for the evaluation of the coefficients in spherical harmonic expansions of functions specified by their values at appropriately chosen points on $S^2$ (known as the forward spherical harmonic transform). The procedure is numerically stable and requires an amount of CPU time proportional to $N^2 (\log N) \log(1/\epsilon)$, where $N^2$ is the number of nodes in the discretization of $S^2$, and $\epsilon$ is the precision of computations. The performance of the algorithm is illustrated via several numerical examples.