MPI/OpenMP-Based Parallel Solver for Imprint Forming Simulation

Abstract

In this research, we present the pure open multi-processing (OpenMP), pure message passing interface (MPI), and hybrid MPI/OpenMP parallel solvers within the dynamic explicit central difference algorithm for the coining process to address the challenge of capturing fine relief features of approximately 50 microns. Achieving such precision demands the utilization of at least 7 million tetrahedron elements, surpassing the capabilities of traditional serial programs previously developed. To mitigate data races when calculating internal forces, intermediate arrays are introduced within the OpenMP directive. This helps ensure proper synchronization and avoid conflicts during parallel execution. Additionally, in the MPI implementation, the coins are partitioned into the desired number of regions. This division allows for efficient distribution of computational tasks across multiple processes. Numerical simulation examples are conducted to compare the three solvers with serial programs, evaluating correctness, acceleration ratio, and parallel efficiency. The results reveal a relative error of approximately 0.3% in forming force among the parallel and serial solvers, while the predicted insufficient material zones align with experimental observations. Additionally, speedup ratio and parallel efficiency are assessed for the coining process simulation. The pure MPI parallel solver achieves a maximum acceleration of 9.5 on a single computer (utilizing 12 cores) and the hybrid solver exhibits a speedup ratio of 136 in a cluster (using 6 compute nodes and 12 cores per compute node), showing the strong scalability of the hybrid MPI/OpenMP programming model. This approach effectively meets the simulation requirements for commemorative coins with intricate relief patterns.