Article in The International Journal of High Performance Computing Applications

Semi-Lagrangian 4d, 5d, and 6d kinetic plasma simulation on large scale GPU equipped supercomputer

By Alexander Moriggl

To simulate the evolution of plasma (a mix of charged particles consisting of ions and electrons), often
kinetic equations, which are a generalization of Newton's law (F = ma) when vast amounts of particles
are considered, have to be solved. The resulting equation is six-dimensional since the plasma depends on
space and velocity. Such high-dimensional problems are challenging since a lot of memory is required. For
example, using a grid of 200 points in each direction requires 512 terabytes of memory. Consequently, we
have to rely on supercomputers. The hardware architecture of such powerful computing devices improved
and changed over time (from sequential to parallel computing). Currently, often even graphic processing
units (GPUs) are used to obtain even more performance. Therefore, new numerical methods that can
exploit such massively parallel systems have to be developed. We have analyzed the performance of a
relatively new numerical scheme (the semi-Lagrangian discontinuous Galerkin method) to solve kinetic
equations and have shown that our code achieves excellent performance on GPUs and scales well up to
1536 GPUs.

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