# Semi-Lagrangian Vlasov simulation on GPUs

## TL;DR

This paper presents an efficient GPU implementation of a semi-Lagrangian discontinuous Galerkin scheme for solving the high-dimensional Vlasov equation, achieving significant speedups and demonstrating good performance across various GPU architectures.

## Contribution

The paper introduces a GPU-accelerated, dimension-independent SLDG code for Vlasov simulations, achieving high performance and portability across different hardware.

## Key findings

- Achieves 470 GB/s on a single GPU and 1600 GB/s on four V100 GPUs.
- Provides a speedup of about ten times over CPU-based solutions.
- Demonstrates effective performance with single precision and across multiple dimensions.

## 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.