Parallel computation for spherical harmonic synthesis and analysis

The objectives of this research were to develop computational techniques for parallel computers capable of performing computations of spherical harmonic analysis and synthesis for ultra-high degree and order. The FFT method was used as a basis for the numerical scheme. The numerical stability of computing-associated Legendre functions and their integrals with both double and quadruple precision was investigated. The domain decomposition and collective communication strategy was used to achieve parallelism and was implemented by message passing. The experimental results showed that the parallel computations significantly shortened computation time and obtained a good implementation with high parallel efficiency.