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.

[1]  Shao-Liang Zhang,et al.  GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems , 1997, SIAM J. Sci. Comput..

[2]  Kengo Nakajima,et al.  The Impact of Parallel Programming Models on the Linear Algebra Performance for Finite Element Simulations , 2006 .

[3]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[4]  Tayfun E. Tezduyar,et al.  A robust preconditioner for fluid–structure interaction problems , 2005 .

[5]  Yousef Saad,et al.  A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition , 2006, SIAM J. Sci. Comput..

[6]  Clayton V. Deutsch,et al.  Geostatistical Software Library and User's Guide , 1998 .

[7]  Kengo Nakajima.  Parallel Preconditioning Methods with Selective Fill-Ins and Selective Overlapping for Ill-Conditioned Problems in Finite-Element Methods , 2007, International Conference on Computational Science.

[8]  Kengo Nakajima.  Parallel Iterative Solvers of GeoFEM with Selective Blocking Preconditioning for Nonlinear Contact Problems on the Earth Simulator , 2003, SC.

[9]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[10]  Rolf Rabenseifner,et al.  Communication Bandwidth of Parallel Programming Models on Hybrid Architectures , 2009, ISHPC.

[11]  Kengo Nakajima,et al.  The Impact of Parallel Programming Models on the Performance of Iterative Linear Solvers for Finite Element Applications , 2006, VECPAR.