The ECHO code for GRMHD: acceleration on GPUs

The Eulerian Conservative High Order (ECHO) code for astrophysical plasmas, solving the equations for classic, special, and general relativistic magnetohydrodynamics, has been developed in Florence since 2000, and its main characteristic features (high order finite-difference reconstruction, two-wave Riemann solver, upwind constrained transport method to preserve a divergence-less magnetic field) are nowadays part of many other successful MHD and GRMHD codes. Here we describe the recent porting of ECHO on GPU accelerated devices, simply based on ISO modern Fortran constructs (namely do concurrent multi-dimensional loops and pure procedures). The accelerated version of the code runs up to 38 times faster than on standard cores (in a test using 4003 cells per GPU versus 2003 per core of the Leonardo pre-exascale supercomputer at Cineca, where each node has 4 NVIDIA A100 GPUs and 32 cores), reaching a maximum efficiency of about 0.22 billion cell updates per node per second (for a full Runge-Kutta iteration, evolving 9 variables). Weak scaling efficiency is above 90% up to at least 64 GPUs, and 70% for 1024 GPUs. Future applications are also briefly discussed.