Parallelization of Two- and Three-Dimensional Fast Fourier Transforms

Abstract : Large computational programs employing multi-dimensional spectral techniques for numerical modeling or image processing rely heavily on the use of Fast Fourier Transforms (FFTs). This report describes work performed to port Numeric Algorithms Group, Ltd. (NAG) two-dimensional and three-dimensional FFTs to the IBM SP-l distributed parallel computing platform to transform arrays of almost any dimension upon many processors, while achieving significant speed-up factors. A description of the parallelization strategies used, observed performance, and conclusions derived is provided. The parallel FFT performance achieved is significant in that it allows for flexible, portable, and robust use of spectral and image processing codes across arbitrary arrays of processors. This further allows for more basic scientific research and production computing with greater flexibility than before. The work described by this report indicates that there is a great potential in implementing flexible and efficient FFTs that can meet the ever-increasing demands of future image and digital signal processing systems.