Systematic Reduction of Data Movement in Algebraic Multigrid Solvers

Algebraic Multigrid (AMG) solvers find wide use in scientific simulation codes. Their ideal computational complexity makes them especially attractive for solving large problems on parallel machines. However, they also involve a substantial amount of data movement, posing challenges to performance and scalability. In this paper, we present an algorithm that provides a systematic means of reducing data movement in AMG. The algorithm operates by gathering and redistributing the problem data to reduce the need to move it on the communication-intensive coarse grid portion of AMG. The data is gathered in a way that ensures data locality by keeping data movement confined to specific regions of the machine. Any decision to gather data is made systematically through the means of a performance model. This approach results in substantial speedups on a multicore cluster when using AMG to solve a variety of test problems.