Parallel Fourier Transformations using shared memory nodes

The Fast Fourier Transform (FFT) is of great importance for various scientific applications used in High Performance Computing (HPC). However, a detailed performance analysis shows that the FFT routines used in these applications, prevent them from scaling to large processor counts. The All-to-All type communication required inside these transformation routines, which becomes extremely costly when large processor counts are involved, seems to be the limiting factor. In the scope of this dissertation, we mainly focus on whether and how the performance of the parallel two-dimensional (2D) FFT can be improved, by exploiting the access to the shared memory nodes of HPCx, a cluster of POWER 5 SMP nodes. In particular, we investigate how to efficiently transfer the data between the processing elements involved in the parallel 2D FFT. Different OpenMP strategies are proposed for the parallelisation of the 2D FFT. The results demonstrate that, for certain problem sizes between 16 and 8192, the access to the shared memory of an HPCx node (16 processors) can produce gains in performance compare to the MPI implementation. In addition, for large processors counts, we use our results from the 2D case to optimise the parallelisation of the three-dimensional (3D) FFT with the Hybrid, a mixed mode programming model between shared memory programming and messaging passing. In our implementation, we use the Master-only style, a version of the Hybrid model, where the MPI communication is handled only by the master thread, outside the OpenMP parallel regions. The results demonstrate a good scaling of the code for problem sizes between 64 and 512 up to 1024 processors. The performance comparisons illustrate that, in certain cases, the Hybrid model can prove beneficial compare to the 2D data decomposition with pure MPI. Subject area: High Performance Computing