Algebraic Multigrid Solver Using Coarse Grid Aggregation with Independent Aggregation
Naoya Nomura, Akihiro Fujii, Teruo Tanaka, Osni Marques, Kengo Nakajima · 2018
The algebraic multigrid (AMG) method is known to be one of the most efficient linear solvers, as it has O(n) complexity and also offers domain parallelism. However, its coarse grids sometimes become more unstructured than the finer grids, which leads to performance degradation, especially when AMG is executed on highly parallel machines. Here, we propose the Coarse Grid Aggregation (CGA) approach that doesn't need coarser level matrix re-distribution. Our approach actually connects process domains using information of edges between process domains. It can adjusts the degree of parallelization for coarser grids by changing the interpolation matrix P and the block row widths of the coarser level matrix. We propose independent aggregation with CGA to enhance the performance of AMG by up to a factor of 3 for the Poisson equation with varying heterogeneous diffusion coefficients. The performance is evaluated on a Fujitsu-FX10 that has more than four thousand nodes consisting of 16-core SPARC64 IXfx CPU. In addition, we check the performance behavior depending on the CGA parameter that is the number of unknowns to be left on one process domain at coarser levels, and consider the tuning of this parameter.