1. A method for efficiently implementing a multidimensional Fast Fourier Transform (FFT) of a multidimensional array comprising a plurality of elements initially distributed in a multi-node computer system comprising a plurality of nodes in communication over a network, the method comprising: (a) distributing the plurality of elements of the array in a first dimension across the plurality of nodes of the computer system over the network to facilitate a first one-dimensional FFT, said computer system comprising a distributed-memory parallel supercomputer, each of said plurality of nodes including at least one processor that operates on a local memory; (b) performing the first one-dimensional FFT on the elements of the array distributed at each node in the first dimension; (c) re-distributing the one-dimensional FFT-transformed elements at each node in a second dimension via “all-to-all” distribution in random order across other nodes of the computer system over the network; and (d) performing a second one-dimensional FFT on elements of the array re-distributed at each node in the second dimension, wherein the random order facilitates efficient utilization of the network thereby efficiently implementing the multidimensional FFT.