Before revision: In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT) that can be used in numerical simulations of partial differential equations . Explicitly vectorized variations of the Gauss-Legendre algorithm are discussed and implemented in the open-source library SHTns which includes scalar and vector transforms.
After revision: In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT) that can be used in numerical simulations of partial differential equations . Explicitly vectorized variations of the algorithm based on the Gauss-Legendre quadrature are discussed and implemented in the open-source library SHTns which includes scalar and vector transforms.