αSetup-AMG: an adaptive-setup-based parallel AMG solver for sequence of sparse linear systems

The algebraic multigrain (AMG) is one of the most frequently used algorithms for the solution of large-scale sparse linear systems in many realistic simulations of science and engineering applications. However, as the concurrency of supercomputers increasing, the AMG solver increasingly leads to poor parallel scalability due to its coarse-level construction in the setup phase. In this paper, to improve the parallel scalability of the traditional AMG to solve the sequence of sparse linear systems arising from PDE-based simulations, we propose a new AMG procedure called αSetup-AMG based on an adaptive setup strategy. The main idea behind αSetup-AMG is the introduction of a setup condition in the coarsening process so that the setup is constructed as it needed instead of constructing in advance via an independent phase in the traditional procedure. As a result, αSetup-AMG requires fewer setup cost and level numbers for the sequence of linear systems. The numerical results on thousands of cores for a radiation hydrodynamics simulation in the inertial confinement fusion (ICF) application show the significant improvement in the efficiency of the αSetup-AMG solver.