Advertisement

A Scalable Parallel Gauss-Seidel and Jacobi Solver for Animal Genetics

  • Martin Larsen
  • Per Madsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1697)

Abstract

A parallel solver based on data parallelism on distributed memory architectures is described. The familiar Gauss-Seidel and Jacobi iterations are used in an “iteration on data” scheme. Minimalization of interprocessor communication is obtained by a split of equations in two sets: Local and Global. Only members of the global set receive contributions from data on more than one processor, hence only global equations require communication during iterations for their solution. Linear and in some models even super linear scalability is obtained in a wide range of model sizes and numbers of parallel processors. The largest example tested in this study is a 3-trait calculation with 30.1 mio. equations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Henderson C.R., 1973. Sire evaluation and genetic trends. In Proc. of the Animal Breeding and Genetics Symposium in Honor of Dr. D.L.Lush. ASAS and ADSA, Champaign, Ill.Google Scholar
  2. 2.
    Henderson C.R., 1976. A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values. Biom. 32:69–83zbMATHGoogle Scholar
  3. 3.
    Larsen M. and P. Madsen, 1999. The CEBUS project: History and overview. Proc. of the CCB’99 International Workshop on High Performance Computing and New statistical Methods in Dairy Cattle Breeding. Interbull Bulletin. In print.Google Scholar
  4. 4.
    Madsen P. and M. Larsen, 1999. Attacking the problem of scalability in parallel Gauss-Seidel and Jacobi solvers for mixed model equations. Proc. of the CCB’99 International Workshop on High Performance Computing and New statistical Methods in Dairy Cattle Breeding. Interbull Bulletin. In print.Google Scholar
  5. 5.
    Schaeffer L.R. and B.W. Kennedy., 1986. Computing Solutions to Mixed Model Equations. Proc. 3.rd. World Congr. on Genetics Applied to Livest. Prod. 12, 382–393. Nebraska.Google Scholar
  6. 6.
    Misztal, I. and D. Gianola, 1987. Indirect Solution of Mixed Model Equations. J. Dairy Sci. 70, 716–723.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Martin Larsen
    • 1
  • Per Madsen
    • 2
  1. 1.UNI•CDanish Computing Centre for Research and EducationLyngbyDenmark
  2. 2.Research Centre FoulumDanish Institute for Agricultural Sciences (DIAS)TjeleDenmark

Personalised recommendations