Topology-Aware Mappings for Large-Scale Eigenvalue Problems

  • Hasan Metin Aktulga
  • Chao Yang
  • Esmond G. Ng
  • Pieter Maris
  • James P. Vary
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7484)

Abstract

Obtaining highly accurate predictions for properties of light atomic nuclei using the Configuration Interaction (CI) approach requires computing the lowest eigenvalues and associated eigenvectors of a large many-body nuclear Hamiltonian matrix, \(\hat{H}\). Since \(\hat{H}\) is a large sparse matrix, a parallel iterative eigensolver designed for multi-core clusters is used. Due to the extremely large size of \(\hat{H}\), thousands of compute nodes are required. Communication overhead may hinder the scalability of the eigensolver at such scales. In this paper, we discuss how to reduce such overhead. In particular, we quantitatively show that topology-aware mapping of computational tasks to physical processors on large-scale multi-core clusters may have a significant impact on efficiency. For typical large-scale eigenvalue calculations, we obtain up to a factor of 2.5 improvement in overall performance by using a topology-aware mapping.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hoefler, T., Snir, M.: Generic Topology Mapping Strategies for Large-scale Parallel Architectures. In: Proceedings of the 2011 ACM International Conference on Supercomputing (ICS), Tucson, AZ (June 2011)Google Scholar
  2. 2.
    Bhatele, A., Gupta, G., Kale, L.V., Chung, I.-H.: Automated Mapping of Regular Communication Graphs on Mesh Interconnects. In: Proceedings of International Conference on High Performance Computing, HiPC (2010)Google Scholar
  3. 3.
    NERSC, Hopper, NERSC’s Cray XE6 System (January 2012), Web. (February 15, 2012), http://www.nersc.gov/users/computational-systems/hopper/.
  4. 4.
    Demmel, J.: Applied Numerical Linear Algebra, 1st edn. SIAM (1997)Google Scholar
  5. 5.
    MPICH2, MPICH2: High-performance and Widely Portable MPI, http://www.mcs.anl.gov/research/projects/mpich2
  6. 6.
    Sternberg, P., Ng, E.G., Yang, C., Maris, P., Vary, J.P., Sosonkina, M., Le, H.V.: Accelerating Configuration Interaction Calculations for Nuclear Structure. In: The Proceedings of the 2008 ACM/IEEE Conference on Supercomputing (SC 2008) (2008)Google Scholar
  7. 7.
    Maris, P., Sosonkina, M., Vary, J.P., Ng, E.G., Yang, C.: Scaling of ab-initio nuclear physics calculations on multicore computer architectures. Procedia CS 1, 97–106 (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hasan Metin Aktulga
    • 1
  • Chao Yang
    • 1
  • Esmond G. Ng
    • 1
  • Pieter Maris
    • 2
  • James P. Vary
    • 2
  1. 1.Lawrence Berkeley National LaboratoryBerkeleyUSA
  2. 2.Iowa State UniversityAmesUSA

Personalised recommendations