High-dimensional grid-based simulations serve as both a tool and a challenge in researching various domains. The main challenge of these approaches is the well-known curse of dimensionality, amplified by the need for fine resolutions in high-fidelity applications. The combination technique (CT) provides a straightforward way of performing such simulations while alleviating the curse of dimensionality. Recent work demonstrated the potential of the CT to join multiple systems simultaneously to perform a single high-dimensional simulation. This paper shows how to extend this to three or more systems and addresses some remaining challenges: load balancing on heterogeneous hardware; utilizing compression to maximize the communication bandwidth; efficient I/O management through hardware mapping; and improving memory utilization through algorithmic optimizations. Combining these contributions, we demonstrate the feasibility of the CT for extreme-scale Superfacility scenarios of 46 trillion DOF on two systems and 35 trillion DOF on three systems. Scenarios at these resolutions would be intractable with full-grid solvers ($\gt1,000$ nonillion DOF each).

Abstract With ever-increasing computational power, larger computational domains are employed and thus the data output grows as well. Writing this data to disk can become a significant part of runtime if done serially. Even if the output is done in parallel, e.g., via MPI I/O, there are many user-space parameters for tuning the performance. This paper focuses on the available parameters for the Lustre file system and the Cray MPICH implementation of MPI I/O. Experiments on the Cray XC40 Hazel Hen using a Cray Sonexion 2000 Lustre file system were conducted. In the experiments, the core count, the block size and the striping configuration were varied. Based on these parameters, heuristics for striping configuration in terms of core count and block size were determined, yielding up to a 32-fold improvement in write rate compared to the default. This corresponds to 85 GB/s of the peak bandwidth of 202.5 GB/s. The heuristics are shown to be applicable to a small test program as well as a complex application.