Modeling the performance of an algebraic multigrid cycle on HPC platforms

Authors:
Hormozd Gahvari;Allison H. Baker;Martin Schulz;Ulrike Meier Yang;Kirk E. Jordan;William Gropp
Affiliations:
University of Illinois at Urbana-Champaign, Urbana, IL, USA;Lawrence Livermore National Laboratory, Livermore, CA, USA;Lawrence Livermore National Laboratory, Livermore, CA, USA;Lawrence Livermore National Laboratory, Livermore, CA, USA;IBM TJ Watson Research Center, Cambridge, MA, USA;University of Illinois at Urbana-Champaign, Urbana, IL, USA
Venue:
Proceedings of the international conference on Supercomputing
Year:
2011

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Abstract

Now that the performance of individual cores has plateaued, future supercomputers will depend upon increasing parallelism for performance. Processor counts are now in the hundreds of thousands for the largest machines and will soon be in the millions. There is an urgent need to model application performance at these scales and to understand what changes need to be made to ensure continued scalability. This paper considers algebraic multigrid (AMG), a popular and highly efficient iterative solver for large sparse linear systems that is used in many applications. We discuss the challenges for AMG on current parallel computers and future exascale architectures, and we present a performance model for an AMG solve cycle as well as performance measurements on several massively-parallel platforms.