Evaluation of Parallel Aggregate Creation Orders: Smoothed Aggregation Algebraic Multigrid Method

  • Akihiro Pujii
  • Akira Nishida
  • Yoshio Oyanagi
Part of the IFIP — The International Federation for Information Processing book series (IFIPAICT, volume 172)


The Algebraic MultiGrid method (AMG) has been studied intensively as an ideal solver for large scale Poisson problems. The Smoothed Aggregation Algebraic MultiGrid (SA-AMG) method is one of the most efficient of these methods. The aggregation procedure is the most important part of the method and is the main area of interest of several researchers.

Here we investigate aggregate creation orders in the aggregation procedure. Five types of aggregation procedure are tested for isotropic, anisotropic and simple elastic problems. As a result, it is important that aggregates are created around one aggregate in each domain for isotropic problems. For anisotropic problems, aggregates around domain borders influence the convergence much. The best strategy for both anisotropic and isotropic problems in our numerical test is the aggregate creation method which creates aggregates on borders first then creates aggregates around one aggregate in the internal domain.

In our test, the SA-AMG preconditioned Conjugate Gradient (CG) method is compared to the Localized ILU preconditioned CG method. In the experiments, Poisson problems up to 1.6 × 107 DOF are solved on 125PEs.


AMG Poisson Solver Aggregate Creation 


  1. [Ada98]
    M. F. Adams. A parallel maximal independent set algorithm. In Proceedings 5th Copper mountain conference on iterative methods, 1998.Google Scholar
  2. [Geo]
    GeoFEM, Scholar
  3. [GGJ+97]_Anshul Gupta, Fred Gustavson, Mahesh Joshi, George Karypis, and Vipin Kumar. Design and implementation of a scalable parallel direct solver for sparse symmetric positive definite systems. In Proceedings of the Eighth SIAM Conference on Parallel Processing, 3 1997.Google Scholar
  4. [MPI]
    MPI(Message Passing Interface) Forum Web Site, Scholar
  5. [Myr]
    Myrinet Software, Scholar
  6. [Nak03]
    K. Nakajima. Parallel Iterative Linear Solvers with Preconditioning for Large Scale Problems. Ph.D. dissertation, University of Tokyo, 2003.Google Scholar
  7. [NNT97]
    K. Nakajima, H. Nakamura, and T. Tanahashi. Parallel iterative solvers with localize ILU preconditioning. In Lecture Notes in Computer Science 1225, pages 342–350, 1997.Google Scholar
  8. [NO99]
    K. Nakajima and H. Okuda. Parallel iterative solvers with Localized ILU preconditioning for unstructured grids on workstation clusters. IJCFD, 12:315–322, 1999.Google Scholar
  9. [TT00]
    Ray S. Tuminaro and Charles Tong. Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines. In SuperComputing, 2000.Google Scholar
  10. [VBM01]
    Petr Vanek, Marian Brezina, and Jan Mandel. Convergence of algebraic multigrid based on smoothed aggregation. Numerische Mathematic, 88(3):559–579, 2001.MathSciNetCrossRefGoogle Scholar

Copyright information

© International Federation for Information Processing 2005

Authors and Affiliations

  • Akihiro Pujii
    • 1
    • 2
  • Akira Nishida
    • 2
    • 3
  • Yoshio Oyanagi
    • 3
  1. 1.The Center for Continuing Professional DevelopmentKogakuin UniversityTokyoJapan
  2. 2.CREST, JSTSaitamaJapan
  3. 3.Department of Computer Science, Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan

Personalised recommendations