Implementation of parallel FFT algorithms on distributed memory machines with a minimum overhead of communication

We present in this paper methods for the many mono-dimensional and multi-dimensional FFT algorithms which minimize the communication overhead. We describe the implementation of these algorithms on a hypercube architecture. Moreover, we derive these implementations onto mesh and torus topologies by using emulation results of hypercube communications on these topologies, We compute optimal sizes of blocks in order to obtain a maximal overlap of communications by computations, Experimental results on Intel iPSC/860 and Paragon, IBM SP1 and Gray T3D machines are given, which confirm the theoretical analysis.