Parallel Multistage Preconditioners Based on a Hierarchical Graph Decomposition for SMP Cluster Architectures With a Hybrid Parallel Programming Model

In this work, the Parallel Hierarchical Interface Decomposition Algorithm (PHIDAL) and a hybrid parallel programming model were applied to finite-element based simulations of linear elasticity problems in media with heterogeneous material properties using parallel preconditioned iterative solvers. Reverse Cuthill-McKee reordering with cyclic multicoloring (CM-RCM) was applied for parallelism on each SMP node through OpenMP. The developed code has been tested on the IBM p5-575 and the TSUBAME Grid Cluster using up to 512 cores. Preconditioners based on PHIDAL provide a superior scalable performance and robustness on both architectures in comparison to conventional block Jacobi-type localized preconditioners.