HPC in Asia:
(A04) Poster from Japan: ppOpen-SOL: Robust ILU Preconditioner for Exascale
TimeWednesday, June 27th10am - 11am
LocationAnalog 1, 2
DescriptionAn objective of this study is to solve generalized eigenvalue problems derived from quantum simulations with exascale systems. To solve eigenvalue problems, we use Sakurai-Sugiura or FEAST method because of versatile. However, we have to solve large-scale systems of linear equations which have ill-conditioned and sparse coefficient matrices. Then, we considered the applicability of a multi-color parallelized ILU preconditioned Krylov subspace method. To improve robustness we applied regularizations to the ILU preconditioner, and to support massive parallelism, we proposed a hierarchical parallelization for multi-coloring algorithms.
If conventional ILU factorization methods are applied to target applications, there are many problems, such as accumulation of rounding error, a breakdown of factorization, etc. We proposed the two types of regularization methods for overcoming such problems, (1) blocking and (2) diagonal shifting of coefficient matrices. These regularization methods provide conventional ILU preconditioned Krylov subspace method with excellent robustness.
For massive parallelism, we proposed a new hierarchical multi-coloring method in the ILU preconditioner. The multicolor is often used for parallelization of ILU factorizations and forward-backward substitutions. Coloring algorithms have much impact on convergence rate and performance of the ILU preconditioned Krylov subspace method. The multi-coloring with hierarchical parallelization has a small influence on convergence rate.
We evaluated the proposed method by the graphene applications with 500M DOF on the Fujitsu PRIMEHPC FX10 supercomputer. By both the approaches, the number of iterations on each number of processes does not differ much. In addition, excellent parallel performance up to 4,800 nodes (76,800cores) has been obtained.