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We describe a methodology for designing efficient parallel and distributedscientific software. This methodology utilizes sequences of mechanizablealgebra--based optimizing transformations. In this study, we apply ourmethodology to the FFT, starting from a high--level algebraic algorithmdescription. Abstract multiprocessor plans are developed and refined to specifywhich computations are to be done by each processor. Templates are then createdthat specify the locations of computations and data on the processors, as wellas data flow among processors. Templates are developed in both the MPI andOpenMP programming styles.  Preliminary experiments comparing code constructed using our methodology withcode from several standard scientific libraries show that our code is oftencompetitive and sometimes performs better. Interestingly, our code handled alarger range of problem sizes on one target architecture.

A Transformation--Based Approach for the Design of Parallel/Distributed Scientific Software: the FFT