Semi-Lagrangian Vlasov simulation on GPUs

Lukas Einkemmer

doi:10.1016/j.cpc.2020.107351

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arXiv · 1907.08316

Semi-Lagrangian Vlasov simulation on GPUs

Lukas Einkemmer

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Abstract

In this paper, our goal is to efficiently solve the Vlasov equation on GPUs. A semi-Lagrangian discontinuous Galerkin scheme is used for the discretization. Such kinetic computations are extremely expensive due to the high-dimensional phase space. The SLDG code, which is publicly available under the MIT license abstracts the number of dimensions and uses a shared codebase for both GPU and CPU based simulations. We investigate the performance of the implementation on a range of both Tesla (V100, Titan V, K80) and consumer (GTX 1080 Ti) GPUs. Our implementation is typically able to achieve a performance of approximately 470 GB/s on a single GPU and 1600 GB/s on four V100 GPUs connected via NVLink. This results in a speedup of about a factor of ten (comparing a single GPU with a dual socket Intel Xeon Gold node) and approximately a factor of 35 (comparing a single node with and without GPUs). In addition, we investigate the effect of single precision computation on the performance of the SLDG code and demonstrate that a template based dimension independent implementation can achieve good performance regardless of the dimensionality of the problem.

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Lukas Einkemmer. 2019-07-18. Semi-Lagrangian Vlasov simulation on GPUs. https://doi.org/10.1016/j.cpc.2020.107351

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