On shared memory parallel computers (SMPCs) it is natural to focus on decomposing the computation (mainly by distributing the iterations of the nested Do-Loops). In contrast, on distributed memory parallel computers (DMPCs) the decomposition of computation and the distribution of data must both be handled---in order to balance the computation load and to minimize the migration of data. We propose and validate experimentally a method for handling computations and data synergistically to optimize the overall execution time. The method relies on a number of novel techniques, also presented in this paper. The core idea is to rank the ``importance'' of data arrays in a program and define some of the dominant. The intuition is that the dominant arrays are the ones whose migration would be the most expensive. Using the correspondence between iteration space mapping vectors and distributed dimensions of the dominant data array in each nested Do-loop, we are able to design algorithms for determining data and computation decompositions at the same time. Based on data distribution, computation decomposition for each nested Do-loop is determined based on either the owner computes rule or the owner stores rule with respect to the dominant data array. If all temporal dependence relations across iteration partitions are regular, we use tiling to allow pipelining and overlapping the computation and communication time. However, to use tiling on DMPCs, we needed to extend the existing techniques for determining tiling vectors and tile sizes, as they were originally suited for SMPCs only. The method is illustrated on programs for the 2D heat equation and for the 2D fast Fourier transform both on a linear processor array.