第144回 第3部

A smoothed aggregation algebraic multigrid (SA-AMG) method is among the fastest and scalable solver for large-scale linear equation Ax = b. In this talk, we demonstrate the convergence and parallel performance of our SA-AMG library on the Oakforest-PACS and K computer. SA-AMG was proposed by Petr Vanek et al. in 1992. SA-AMG achieves good convergence and scalability by damping various wavelength components efficiently. To damp these components, SA-AMG creates multi-level matrices with arbitrary policies. The created matrices are hierarchically smaller than the dimension of the original coefficient matrix. By using these multi-level matrices, error components are damped efficiently. To parallelize the SA-AMG method, we applied an OpenMP/MPI hybrid parallelization with a domain decomposition technique. Target applications of our study are large-scale and have geometrical information. On these applications, the hybrid parallelization and the domain decomposition technique are suitable. In this talk, we demonstrate numerical evaluations using Oakforest-PACS (JCAHPC) and K (RIKEN R-CCS) supercomputer system. Each supercomputer system uses cluster architecture by Intel(R) Xeon Phi(TM) and SPARC64 VIIIfx, respectively. The numerical evaluations showed good convergence and parallel performance of our SA-AMG library.