A Low-Communicaton Method to Solve Poisson's Equation on Locally-Structured Grids

Authors: Brian Van Straalen (Lawrence Berkeley National Laboratory), Peter McCorquodale (Lawrence Berkeley National Laboratory), Phil Colella (Lawrence Berkeley National Laboratory), Christos Kavouklis (Lawrence Livermore National Laboratory)

Abstract: This poster describes a new algorithm, Method of Local Corrections (MLC), and a high-performance implementation for solving Poisson's equation with infinite-domain boundary conditions, on locally-refined nested rectangular grids. The data motion is comparable to that of only a single V-cycle of multigrid, and hence is an order of magnitude smaller than traditional multigrid iteration. The computational kernels are 3D FFTs on small domains. Strong scaling tests on 64 to 4096 cores on NERSC Cori I (Haswell) show over 60% efficiency, and weak scaling by replication tests over 64 to 32768 cores show 92% efficiency on the same platform. We find comparable solve times between HPGMG on a uniform grid with one billion grid points, and MLC on the same number of grid points adaptively distributed. MLC is designed for AMR, able to solve problems with much higher resolution at the finest level than an algorithm on a uniform grid.

Best Poster Finalist (BP): no

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