Skip to main content

Frontal software for the solution of sparse linear equations

  • Conference paper
  • First Online:
  • 192 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1184))

Abstract

We discuss the power and limitations of frontal solvers for the solution of large sparse systems of linear equations. We describe their design and user interface. We compare sparse frontal codes from the Harwell Subroutine Library (HSL) against other HSL sparse solvers and consider the effect of ordering on the frontal solver. We consider both the case of assembled and unassembled systems for both symmetric positive-definite and unsymmetric matrices. We use problems arising in real engineering or industrial applications in our tests.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Patrick R. Amestoy and Iain S. Duff. Vectorization of a multiprocessor multifrontal code. Int. J. of Supercomputer Applics., 3:41–59, 1989.

    Google Scholar 

  2. A. C. Damhaug and J. K. Reid. MA46, a Fortran code for direct solution of sparse unsymmetric linear systems of equations from finite-element applications. Technical Report RAL-TR-96-10, Rutherford Appleton Laboratory, 1996.

    Google Scholar 

  3. Jack J. Dongarra, Jeremy Du Croz, Iain S. Duff, and Sven Hammarling. A set of Level 3 Basic Linear Algebra Subprograms. ACM Trans. Math. Softw., 16:1–17, 1990.

    Google Scholar 

  4. Iain S. Duff. Design features of a frontal code for solving sparse unsymmetric linear systems out-of-core. SIAM J. Scientific and Statistical Computing, 5:270–280, 1984.

    Google Scholar 

  5. Iain S. Duff, Roger G. Grimes, and John G. Lewis. Sparse matrix test problems. ACM Trans. Math. Softw., 15(1):1–14, March 1989.

    Google Scholar 

  6. Iain S. Duff, Roger G. Grimes, and John G. Lewis. Users' guide for the Harwell-Boeing sparse matrix collection (Release I). Technical Report RAL 92-086, Rutherford Appleton Laboratory, 1992.

    Google Scholar 

  7. Iain S. Duff and John K. Reid. MA27 — A set of Fortran subroutines for solving sparse symmetric sets of linear equations. Technical Report AERE R10533, Her Majesty's Stationery Office, London, 1982.

    Google Scholar 

  8. Iain S. Duff and John K. Reid. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Trans. Math. Softw., 9:302–325, 1983.

    Google Scholar 

  9. Iain S. Duff and John K. Reid. MA48, a Fortran code for direct solution of sparse unsymmetric linear systems of equations. Technical Report RAL 93-072, Rutherford Appleton Laboratory, 1993.

    Google Scholar 

  10. Iain S. Duff and John K. Reid. The design of MA48, a code for the direct solution of sparse unsymmetric linear systems of equations. ACM Trans. Math Softw., 22(2):187–226, 1996.

    Google Scholar 

  11. Iain S. Duff, John K. Reid, and Jennifer A. Scott. The use of profile reduction algorithms with a frontal code. Int J. Numerical Methods in Engineering 28:2555–2568, 1989.

    Google Scholar 

  12. Iain S. Duff and Jennifer A. Scott. MA42 — a new frontal code for solving sparse unsymmetric systems. Technical Report RAL 93-064, Rutherford Appleton Laboratory, 1993.

    Google Scholar 

  13. Iain S. Duff and Jennifer A. Scott. The use of multiple fronts in Gaussian elimination. In J. G. Lewis, editor, Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, pages 567–571, Philadelphia, 1994. SIAM Press.

    Google Scholar 

  14. Iain S. Duff and Jennifer A. Scott. The design of a new frontal code for solving sparse unsymmetric systems. ACM Trans. Math. Softw., 22(1):30–45, 1996.

    Google Scholar 

  15. Iain S. Duff and Jennifer A. Scott. MA62 — a frontal code for sparse positive-definite symmetric systems from finite-element applications. Technical Report To appear, Rutherford Appleton Laboratory, 1996.

    Google Scholar 

  16. P. Hood. Frontal solution program for unsymmetric matrices. Int J. Numerical Methods in Engineering, 10:379–400, 1976.

    Google Scholar 

  17. HSL. Harwell Subroutine Library. A Catalogue of Subroutines (Release 12). AEA Technology, Harwell Laboratory, Oxfordshire, England, 1996. For information concerning HSL contact: Dr Scott Roberts, AEA Technology, 552 Harwell, Didcot, Oxon OX11 0RA, England (tel: +44-1235-434714, fax: +44-1235-434136, email: Scott.Roberts@aeat.co.uk).

    Google Scholar 

  18. B. M. Irons. A frontal solution program for finite-element analysis. Int J. Numerical Methods in Engineering, 2:5–32, 1970.

    Google Scholar 

  19. J. A. Scott. Element resequencing for use with a multiple front algorithm. Technical Report RAL-TR-95-029, Rutherford Appleton Laboratory, 1995. To appear in Int J. Numerical Methods in Engineering.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jerzy Waśniewski Jack Dongarra Kaj Madsen Dorte Olesen

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Duff, I.S., Scott, J.A. (1996). Frontal software for the solution of sparse linear equations. In: Waśniewski, J., Dongarra, J., Madsen, K., Olesen, D. (eds) Applied Parallel Computing Industrial Computation and Optimization. PARA 1996. Lecture Notes in Computer Science, vol 1184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62095-8_24

Download citation

  • DOI: https://doi.org/10.1007/3-540-62095-8_24

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62095-2

  • Online ISBN: 978-3-540-49643-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics