Sparse LU factorization with partial pivoting overlapping communications and computations on the SP-2 multicomputer

  • C. N. Ojeda-Guerra
  • E. Macías
  • A. Suárez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1497)


The problem of solving a sparse linear system of equation (A × x=b) is very important in scientific applications and is still an open problem to develop on multicomputer with distributed memory. This paper presents an algorithm for parallelizing the sparse LU on a SP-2 multicomputer using MPI and standard sparse matrices. Our goal is to implement the parallel algorithm studying the dependence graph of the sequential algorithm which drives us to overlap computations and communications. So, this analysis can be performed by an automatic tool that helps us to choose the best data distribution. The paper analyses the effect of several block sizes in the performance results in order to overlap efficiently.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    U. Banerjee: Dependence Analysis for Supercomputing. Kluwer Academic Publishers. (1988)Google Scholar
  2. 2.
    Davis T.A., Duff I.S.: An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization. RAL-93-036. Department for Computation and Information. Atlas Center. Rutherford Appleton Laboratory. (1993)Google Scholar
  3. 3.
    Demmel J.W., Eisenstat S.C., Gilbert J.R., Li X.S., Liu J.W.: A Supernodal Approach to Sparse Partial Pivoting. Technical Report CSD-95-883, UC Berkeley. (1995)Google Scholar
  4. 4.
    Duff I.S.: Sparse Numerical Linear Algebra: Direct Methods and Preconditioning. RAL-TR-96-047. Department for Computation and Information. Atlas Center. Rutherford Appleton Laboratory. (1996)Google Scholar
  5. 5.
    Duff I.S., Reid J.K.: MA48, a Fortran Code for Direct Solution of Sparse Unsymmetric Linear Systems of Equations. Tech. Report RAL-93-072. Rutherford Appleton Lab. (1993)Google Scholar
  6. 6.
    Fu C., Jiao X., Yang T.: Efficient Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures. IEEE Transactions on Parallel and Distributed Systems, vol. 9 no. 2 (1998) 109–126Google Scholar
  7. 7.
    Golub G.H., Van Loan C.F.: Matrix Computations. Second Edition. The Johns Hopkins University Press. (1989)Google Scholar
  8. 8.
    Information available in: Scholar
  9. 9.
    Information available in: Scholar
  10. 10.
    Miguel J., Arrabuena A., Beivide R., Gregorio J.A.: Assesing the Performance of the new IBM SP-2. IEEE Parallel and Distributed Thecnology, vol. 4 no. 4 (1996) 12–33CrossRefGoogle Scholar
  11. 11.
    Suárez A., Ojeda-Guerra C.N.: Overlapping Computations and Communications on Torus Networks. Fourth Euromicro Workshop on Parallel and Distributed Processing. (1996) 162–169Google Scholar
  12. 12.
    Tourino J., Doallo R., Asenjo R., Plata O. y Zapata E.: Analyzing Data Structures for Parallel Sparse Direct Solvers: Pivoting and Fill-in. Sixth Workshop on Compilers for Parallel Computers. (1996) 151–168Google Scholar
  13. 13.
    Li X.S.: Sparse Gaussian Elimination on High Performance Computers. PhD Thesis. University of California at Berkeley. (1996)Google Scholar
  14. 14.
    Xu Z., Wang K.: Modelling communication Overhead: MPI and MPL Performance on the IBM SP-2. IEEE Parallel and Distributed Thecnology, vol. 4 no. 1 (1996) 9–25MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • C. N. Ojeda-Guerra
    • 1
  • E. Macías
    • 1
  • A. Suárez
    • 1
  1. 1.Dpto. de Ingeniería Telemática U.L.P.G.C.Grupo de Arquitectura y Concurrencia (G.A.C.)Spain

Personalised recommendations