Development of Solid Earth Simulation Platform Sparse Approximate Inverse Preconditioner for Contact Problems using OpenMP Project Representative

The three-level hybrid parallel programming model consisting of MPI, OpenMP and vectorization with multicolor-based reordering methods provides optimum performance on SMP cluster architectures with vector processors such as the Earth Simulator (ES) for finite-element type applications. While the three-level hybrid and flat MPI parallel programming models offer similar performance, the hybrid programming model outperforms flat MPI in the problems with large numbers of SMP nodes. In the cases with many colors, fewer numbers of iterations are required for convergence, but the performance is worse due to the smaller loop length and greater overhead. On ES, hybrid parallel programming model is much more sensitive to color number. In this study, SAI (Sparse Approximate Inverse) preconditioning method has been implemented to a single SMP node of ES using OpenMP. Developed method has been tested for applications with contact condition, and demonstrated efficiency and robustness for a wide range of problem size.