Efficient Parallel FFTs for Different Computational Models

We select the Fast Fourier Transform (FFT) to demonstrate a methodology for deriving the optimal parallel algorithm according to predetermined performance metrics, within a computational model. Following the vector space framework for parallel permutations, we provide a specification language to capture the algorithm, derive the optimal parallel FFT specification, compute the arithmetic, memory, communication and load{balance complexity metrics, apply the analytical performance evaluation to PRAM, LPRAM, BSP and LogP computational models, and compare with actual performance results.Engineering and Applied Science

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 log2N). 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.Engineering and Applied Science

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 log² 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