A scalable paradigm for effectively-dense matrix formulated applications

  • G. Cheng
  • G. C. Fox
  • K. A. Hawick
Numerical Algorithms for Engineering
Part of the Lecture Notes in Computer Science book series (LNCS, volume 797)


There is a class of problems in computational science and engineering which require formulation in full matrix form and which are generally solved as dense matrices either because they are dense or because the sparsity can not be easily exploited. Problems such as those posed by computational electromagnetics, computational chemistry and some quantum physics applications frequently fall into this class. It is not sufficient just to solve the matrix problem for these applications as other components of the calculation are usually of equal computational load on current computer systems, and these components are consequently of equal importance to the end user of the application. We describe a general method for programming such applications using a combination of distributed computing systems and of more powerful back-end compute resources to schedule the components of such applications. We show how this not only improves computational performance but by making more memory available, allows hitherto impracticably large problems to be run. We illustrate this problem paradigm and our method of solution with problems in electromagnetics, chemistry and physics, and give a detailed performance analysis of a typical electromagnetics application. We discuss a method for scheduling the computational components using the Application Visualisation System (AVS).


Matrix Assembly Large Problem Size Right Hand Side Vector Heterogeneous Computing System Functional Parallelism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Advanced Visual Systems Inc. AVS 4.0 Developer's Guide, May 1992 and AVS 4.0 User's Guide, May 1992.Google Scholar
  2. 2.
    G. Cheng, Y. Lu, G. C. Fox, K.Mills and T. Haupt, An Interactive Remote Visualisation Environment for an Electromagnetic Scattering Simulation on a High Performance Computing System, Proc. Supercomputing 1993, Portland, Oregon, November 15, 1993, PP317–326.Google Scholar
  3. 3.
    G. Cheng, K. Mills and G. C. Fox, An Interactive Visualisation Environment for Financial Modeling on Heterogeneous Computing Systems, Proc. of the 6th SIAM Conference on Parallel Processing for Scientific Computing, March 1993, Norfolk, VA.Google Scholar
  4. 4.
    J. Choi, J. J. Dongarra, R. Pozo, and D. W. Walker, Scalapack: A scalable linear algebra library for distributed memory concurrent computers. In Proceeding of the Fourth Symposium on the Frontiers of Massively Parallel Computation, PP 120–127. IEEE Computer Society Press, 1992.Google Scholar
  5. 5.
    J. J. Dongarra and R. A. van de Geijn. Two-dimensional basic linear algebra communication subprograms, Technical Report LAPACK working note 37, Computer Science Department, University of Tennessee, Knoxville, TN, October 1991.Google Scholar
  6. 6.
    J. J. Dongarra, R. A. van de Geijn and D. W. Walker, A look at scalable dense linear algebra libraries, in IEEE Proceedings of the Scalable High-Performance Computing Conference, PP372–379, IEEE Publisgers, 1992.Google Scholar
  7. 7.
    I. S. Duff, A. M. Erisman, and J. K. Reid, Direct Methods for Sparse Matrices, Clarendon Press, Oxford 1986.Google Scholar
  8. 8.
    E. R. Davison, Monster Matrices: their eigenvalues and eigenvectors, Computers in Physics, Vol. 7, No. 5, Sep/Oct 1993.Google Scholar
  9. 9.
    E. R. Davison, J. Comput. Phys. 17, 87 (1975); Comput. Phys. Commun. 53, 49 (1989).Google Scholar
  10. 10.
    A. Edelman, Large dense numerical linear algebra in 1993: The parallel computing influence, International Journal of Supercomputing Applications, 1993.Google Scholar
  11. 11.
    G. C. Fox, Parallel Computing in Industry: An Initial Survey, in Proc. of Fifth Australian Supercomputing Conference, World Congress Centre, Melbourne, Australia, December, 1992.Google Scholar
  12. 12.
    R. F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill Book Company, New York (1961).Google Scholar
  13. 13.
    R. F. Harrington, Field Computation by Moment Methods, the Macmillan Co., New York (1968). Reprinted by Krieger Publishing Co., Malabar, FL (1982).Google Scholar
  14. 14.
    R. F. Harrington, Matrix Methods For Field Problems, Proc. IEEE, vol. 55, No. 2, pp. 136–149, Feb. 1967.Google Scholar
  15. 15.
    E. C. Jordon and K. G. Balmain, Electromagnetic Waves and Radiating Systems, Second Edition, Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1969).Google Scholar
  16. 16.
    G. von Laszewski, Parallelization of MOPAC, Northeast Parallel Architecture Center, Technical Report, September 14, 1992.Google Scholar
  17. 17.
    B. Liu, in Numerical Algorithms in Chemistry; Algebraic Methods, edited by C. Moler and I. Shavitt (Lawrence Berkeley Laboratory, Berkeley, CA, 1978).Google Scholar
  18. 18.
    Y. Lu, A. G. Mohamed, G. C. Fox and R. F. Harrington, Implementation of Electromagnetic Scattering from Conductors Containing Loaded Slots on the Connection Machine CM-2, Proc. of the 6th SIAM Conference on Parallel Processing for Scientific Computing, March 1993, Norfolk, VA.Google Scholar
  19. 19.
    Y. Lu and R. F. Harrington, Electromagnetic Scattering from a Plane Conducting Two Slots Terminated by Microwave Network(TE Case), Technical Report, TR-91-2, ECE Department, Syracuse University, August 1991.Google Scholar
  20. 20.
    D. S. Scott and E. Castro-Leon, Solving Large Out of Core Systems of Linear Equations using the iPSC/8609, in Progress in Electromagnetic Research: Computational Electromagnetics and Supercomputer Architecture, edited by Tom Cwik and Jean Patterson, 1992.Google Scholar
  21. 21.
    Silicon Graphics Inc. Iris Explorer User's Guide, 1992.Google Scholar
  22. 22.
    Connection Machine Scientific Software Library (CMSSL), Thinking Machines Corporation, Cambridge, Massachusetts, June 1992.Google Scholar
  23. 23.
    Thinking Machines Corporation, The Connection Machine CM-5 technical summary, Technical Report, Cambridge, MA, pp. 340–353, October 1991.Google Scholar
  24. 24.
    J. Van Bladel and C. M. Butler, Aperture Problems, (Proc. NATO Adv. Study Inst. on Theoretical Methods for Determining the Interaction of Electromagnetic Waves with Structures,) Ed. by J. Skwirzynski, Sythoff and Noordhoff international Publishers, 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • G. Cheng
    • 1
  • G. C. Fox
    • 1
  • K. A. Hawick
    • 1
  1. 1.Northeast Parallel Architectures CenterSyracuse UniversitySyracuseUSA

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