The inherent overlapping in the parallel calculation of the Laplacian

Abstract

A new approach for the parallel computation of the Laplacian in the Fourier domain is presented. This numerical problem inherits the intrinsic sequencing involved in the calculation of any multidimensional Fast Fourier Transform (FFT) where blocking communications assure that its computation is strictly carried out dimension by dimension. Such data dependency vanishes when one considers the Laplacian as the sum of n independent one-dimensional kernels, so that computation and communication can be naturally overlapped with nonblocking communications. Overlapping is demonstrated to be responsible for the speedup figures we obtain when our approach is compared to state-of-the-art parallel multidimensional FFTs.