A General Design for a Scalable MPI-GPU Multi-Resolution 2D Numerical Solver

This article presents a multi-GPU implementation of a Finite-Volume solver on a multi-resolution grid. The implementation completely offloads the computation to the GPUs and communications between different GPUs are implemented by means of the Message Passing Interface (MPI) API. Different domain decomposition techniques have been considered and the one based on the Hilbert Space Filling Curves (HSFC) showed optimal scalability. Several optimizations are introduced: One-to-one MPI communications among MPI ranks are completely masked by GPU computations on internal cells and a novel dynamic load balancing algorithm is introduced to minimize the waiting times at global MPI synchronization barriers. Such algorithm adapts the computational load of ranks in response to dynamical changes in the execution time of blocks and in network performances; Its capability to converge to a balanced computation has been empirically shown by numerical experiments. Tests exploit up to 64 GPUs and 83M cells and achieve an efficiency of 90 percent in weak scalability and 85 percent for strong scalability. The framework is general and the results of the article can be ported to a wide range of explicit 2D Partial Differential Equations solvers.