MHD code using multi graphical processing units: SMAUG+

This paper introduces the Sheffield Magnetohydrodynamics Algorithm Using GPUs (SMAUG+), an advanced numerical code for solving magnetohydrodynamic (MHD) problems, using multi-GPU systems. Multi-GPU systems facilitate the development of accelerated codes and enable us to investigate larger model sizes and/or more detailed computational domain resolutions. This is a significant advancement over the parent single-GPU MHD code, SMAUG (Griffiths, M., Fedun, V., and Erd\'elyi, R. (2015). A fast MHD code for gravitationally stratified media using graphical processing units: SMAUG. Journal of Astrophysics and Astronomy,36(1):197-223). Here, we demonstrate the validity of the SMAUG+ code, describe the parallelisation techniques and investigate performance benchmarks. The initial configuration of the Orszag-Tang vortex simulations are distributed among 4, 16, 64 and 100 GPUs. Furthermore, different simulation box resolutions are applied: $1000 \times 1000$, $2044 \times 2044$, $4000 \times 4000$ and $8000 \times 8000$. We also tested the code with the Brio-Wu shock tube simulations with model size of 800 employing up to 10 GPUs. Based on the test results, we observed speed ups and slow downs, depending on the granularity and the communication overhead of certain parallel tasks. The main aim of the code development is to provide massively parallel code without the memory limitation of a single GPU. By using our code, the applied model size could be significantly increased. We demonstrate that we are able to successfully compute numerically valid and large 2D MHD problems.