OpenMP/MPI Hybrid Parallel ILU(k) Preconditioner for FEM Based on Extended Hierarchical Interface Decomposition for Multi-core Clusters

摘要

While ILU preconditioner is a powerful and popular preconditioning method for Krylov iterative solvers on sparse matrices derived from finite element analysis, it have been exploerd the scalable hybrid parallelization scheme for ILU preconditioner targetting multi/many-core clusters. Hierarchical Interface Decompostion (HID) is a robust and efficient parallel method for ILU preconditioner. The extended version of HID (ExHID), our proposed method, introduces thicker level-2 connector in order to consider fill-ins. Basing on HID and ExHID we developed hybrid parallel ILU preconditioner with fill-ins using OpenMP/MPI hybrid parallel programing models. While inter-node parallelization is based on HID/ExHID, we applied two different methods, multicolor based reordering and HID/ExHID to intra-node parallelization. The two implementations according to different hybrid strategy, HID(inter-node)-HID (intra-node) and HID(inter-node)-MC(intra-node), are evaluated through strong scaling tests and the better hybrid strategy is explored. HID-HID generally results with better convergence and less fill-ins. On the other hand, HID-MC could be more stable strategy than HID-HID when increasing the number of threads per process.