In this paper, we describe the implementation of an AMG solver for a hybrid cluster that exploits distributed and shared memory parallelization and uses the available GPU accelerators on each node. This solver has been written by using LAMA (Library for Accelerated Math Applications). This library does not only provide an easy-to-use framework for solvers that might run on different devices with different matrix formats, but also comes with features to optimize and hide communication and memory transfers between CPUs and GPUs. These features are explained and their impact on the efficiency of the AMG solver is shown in this paper. The benchmark results show that an efficient use of hybrid clusters is even possible for multi-level methods like AMG where fast solutions are needed on all levels for multiple problem sizes.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Open MPI 1.4.4. Tests with Intel MPI 4.0.2.003 showed a similar behavior.
Hypre homepage (2010) https://computation.llnl.gov/casc/hypre/software.html, last viewed Jan 2012
Lama software on Sourceforge (2011) http://www.sourceforge.net/projects/libama, last viewed Jan 2012
ML homepage (2011) http://trilinos.sandia.gov/packages/ml/, last viewed Jan 2012
SAMG homepage (2011) https://www.scai.fraunhofer.de/samg.html, last viewed Jan 2012
Lama homepage (2012) http://www.libama.org, last viewed Jan 2012
MTL4 CG (2012) http://www.simunova.com/en/node/184, last viewed Jan 2012
Ament M, Knittel G, Weiskopf D, Straßer W (2010) A parallel preconditioned conjugate gradient solver or the poisson problem on a multi-GPU platform. In: Parallel, distributed, and network based processing, pp 583–593
Bell N, Garland M (2009) Efficient sparse matrix-vector multiplication on CUDA. In: Proc ACM/IEEE conf supercomputing (SC), Portland, OR, USA
Brandt A, McCormick S, Ruge J (1984) Algebraic Multigrid (AMG) for sparse matrix equations. In: Evans DJ (ed) Sparsity and its Applications. Cambridge University Press, Cambridge
Catalyurek U, Aykanat C (2001) A hypergraph-partitioning approach for coarse-grain decomposition. In: SC2001, Denver, CO. ACM/IEEE, New York
Cevahir A, Nukada A, Matsuoka S (2009) Fast conjugate gradients with multiple GPUs. In: ICCS 2009, vol 5544, pp 893–903
Cevahir A, Nukada A, Matsuoka S (2010) High performance conjugate gradient solver on multi-GPU clusters using hypergraph partitioning. Comput Sci Res Dev 25:83–91
Förster M, Kraus J (2011) Scalable parallel AMG on CCNUMA machines with OpenMP. Springer, Berlin, pp 1–8
Haase G, Liebmann M, Douglas C, Plank G (2010) A parallel algebraic multigrid solver on graphics processing units. In: High performance computing and applications, pp 38–47
Heuveline V, Lukarski D, Weiss JP (2012) Using multicore CPUs and GPUs. Springer, Berlin
Kraus J, Förster M (2012) Efficient AMG on heterogeneous systems Springer, Berlin, pp 133–146
Ruge J, Stüben K (1987) Algebraic Multigrid (AMG). In: McCormick SF (ed) Multigrid methods. Frontiers in applied mathematics, vol 3. SIAM, Philadelphia, pp 73–130
Schubert G, Fehske H, Hager G, Wellein G (2011) Hybrid-parallel sparse matrix-vector multiplication with explicit communication overlap on current multicore-based systems. Parallel Process Lett 21(3):339–358
Strustrup B (2000) The C++ programming language. Special edition
Van Dyk D, Geveler M, Mallach S, Ribbrock D, Göddeke D, Gutwenger C (2009) Honei: a collection of libraries for numerical computations targeting multiple processor architectures. Comput Phys Commun 180(12):2534–2543
Granted by Fraunhofer, ITEA2 project H4H—BMBF 01|S10036H, BMBF project GASPI 01|H11007F.
Rights and permissions
About this article
Cite this article
Kraus, J., Förster, M., Brandes, T. et al. Using LAMA for efficient AMG on hybrid clusters. Comput Sci Res Dev 28, 211–220 (2013). https://doi.org/10.1007/s00450-012-0223-3