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ACMP05 - Efficient, Portable, Massively Parallel Free-Space Solvers for the Poisson Equation

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Vico et al. (2016) suggest a fast algorithm for computing volume potentials which is of benefit to the beam and plasma physics communities, as they require the solution of Poisson’s equation with free-space boundary conditions. The standard method to solve the free-space Poisson equation is to use the algorithm presented by Hockney and Eastwood (1988), which is second order in convergence at best. The algorithm proposed by Vico et al., which we refer to as Vico-Greengard, converges spectrally, i.e. faster than any fixed order of the number of grid points, for smooth enough functions. We implement a performance portable Poisson solver in the framework of the IPPL (Independent Parallel Particle Layer) library based on these two methods: the traditional Hockney-Eastwood, and the novel Vico-Greengard. Furthermore, we suggest an improvement to the Vico-Greengard algorithm which reduces its memory footprint. We show that for sufficiently smooth distribution functions, the Vico-Greengard algorithm could be a good candidate for reducing memory usage, since better accuracy can be obtained with a coarser grid. This is especially significant for GPUs, which present memory constraints. Finally, we showcase performance through scaling studies on the Perlmutter (NERSC) supercomputer, with efficiencies staying above 50% in the strong scaling case.



Paul Scherrer Institute

Sonali studied Physics at the Ecole Polytechnique Fédérale de Lausanne (EPFL), completing her Bachelor and Master with a year abroad at the National University of Singapore. After graduating, she worked as a Research Engineer at the Barcelona Supercomputing Center (BSC), where she carried out performance analysis for climate physics codes. Currently, Sonali is pursuing a PhD in computational physics at the Paul Scherrer Institut/ETH Zürich, focusing on efficient and massively parallel solvers for particle dynamics simulations in the context of HPC.