Scalable parallel FFT for spectral simulations on a Beowulf cluster

The implementation and performance of the multidimensional Fast Fourier Transform (FFT) on a distributed memory Beowulf cluster is examined. We focus on the three-dimensional (3D) real transform, an essential computational component of Galerkin and pseudo-spectral codes. The approach studied is a 1D domain decomposition algorithm that relies on communication-intensive transpose operation involving P processors. Communication is based upon the standard portable message passing interface (MPI). We show that 1/P scaling for execution time at fixed problem size N3 (i.e., linear speedup) can be obtained provided that (1) the transpose algorithm is optimized for simultaneous block communication by all processors; and (2) communication is arranged for non-overlapping pairwise communication between processors, thus eliminating blocking when standard fast ethernet interconnects are employed. This method provides the basis for implementation of scalable and efficient spectral method computations of hydrodynamic and magneto-hydrodynamic turbulence on Beowulf clusters assembled from standard commodity components. An example is presented using a 3D passive scalar code.