We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the FFT, starting from a high--level algebraic algorithm description. Abstract multiprocessor plans are developed and refined to specify which computations are to be done by each processor. Templates are then created that specify the locations of computations and data on the processors, as well as data flow among processors. Templates are developed in both the MPI and OpenMP programming styles. Preliminary experiments comparing code constructed using our methodology with code from several standard scientific libraries show that our code is often competitive and sometimes performs better. Interestingly, our code handled a larger range of problem sizes on one target architecture.