| Abstract: |
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Elliptic equations like Poisson equation have to be solved by using global data in the whole computational domain and thus global communication is essential for the parallel computation. In serial computation, it is well known that there are some O(N) and O(NlogN) methods for solving the elliptic equations such as Fast Fourier Transform (FFT), Multigrid, and Fast Multipole Method (FMM).
In this paper we present preliminary benchmark results of the performance of a Parallel Multigrid Poisson solver on the K computer, RIKEN Japan. We have developed a Parallel Multigrid Poisson solver for massively parallel supercomputer. The Multigrid code is parallelized by both MPI and OpenMP. Up to 12,288 nodes with 98,304 cores, excellent weak scaling is shown. We implement Red and Black data arrays separately in order to reduce cache miss rate for the Red-Black Gauss-Seidel smoother.
For a comparison we have also implemented a Parallel FFT Poisson solver which is well known as an inefficient parallel computation. Using Fujitsu Scientific Subroutine Library “SSL ?” one-dimensional FFT subroutine dvcfm1 we have developed an OpenMP/MPI hybrid parallelized FFT in three-dimension with one-dimensional MPI decomposition. Using OpenMP thread parallelization MPI all-to-all communication is performed on the master thread and FFT calculations are overlapped to the communication. Our implementation has significantly improved the parallel performance compared to the subroutine ds_3dcft provided by SSL?. |
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