Hierarchical Load Balancing for Parallel Fast Legendre Transforms

We present a parallel Fast Legendre Transform (FLT) based on the Driscol--Healy algorithm with computation complexity O(N log 2 N ). The parallel FLT is load-- balanced in a hierarchical fashion. We use a load--balanced FFT to deduce a load-- balanced parallel fast cosine transform, which in turn serves as a building block for the Legendre transform engine, from which the parallel FLT is constructed. We demonstrate how the arithmetic, memory and communication complexities of the parallel FLT are hierarchically derived via the complexity of its modular blocks. 1 Introduction Legendre transforms are ubiquitous in many disciplines of applied sciences, particularly spectral methods for the solution of partial differential equations [3]. For applications of harmonic analysis on the 2--sphere S 2 , an efficient Legendre transform is as crucial to numeric computation as the fast Fourier transform (FFT) is to classical time--series analysis on R. This stems from the fact that harmonic ana...