GPU Accelerated Reduced MHD Simulations: An Application to Magnetic Island Coalescence in 3D Line-Tied Geometry

We present a comprehensive re-programming of a 3D reduced MHD code for hardware acceleration using graphics processing units (GPUs) with Nvidia CUDA. The code (pseudo-spectral semi-implicit) is tailored for the study of a 3D model of coronal heating [Arxiv:1106.0515]. We discuss our general porting strategy and report code performance and detailed code tracing on GPU accelerated supercomputers (NCSA/Forge, NICS/Keeneland). At $2048^{2}\times256$, the highest resolution tested, the chip-to-chip speedup is $18\times$ comparing Xeon Nehalem QC and Nvidia Fermi. Scaling well up to $256$ GPUs, the code effectively gives a speedup of $46\times$ compared with our original code on a conventional CPU cluster. A test case is presented in which magnetic island coalescence is studied in 3D line-tied geometry, where very large Lundquist numbers are used to induce magnetic flux-tube sloshing. Results are compared with existing 2D simulations and the advantages of the GPU implementation are emphasized.