Advertisement

The Journal of Supercomputing

, Volume 40, Issue 1, pp 67–80 | Cite as

Supercomputing applications to the numerical modeling of industrial and applied mathematics problems

  • Juan A. Acebrón
  • Renato Spigler
Article

Abstract

Present and future supercomputers offer many opportunities and advantages to attack complex and demanding industrial and applied mathematical problems, but provide also new challenges. In the Peta-Flops regime, these concern both, the way to exploit the increasingly available power and the need of designing algorithms which are scalable and fault-tolerant at the same time. An example of a probabilistic domain decomposition method, which is indeed scalable and naturally fault-tolerant, is presented. Grid computing should also be mentioned as an increasingly popular way to perform massively distributed computing: it represents a way to exploit computing power, aside the existing supercomputers. Beyond classical supercomputers there is the prospective quantum computer, in view of which it is advisable to start now a search for suitable algorithms for certain classes of problems.

Keywords

Supercomputers Supercomputing Parallel computing Monte Carlo methods Scalability Fault-tolerance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Acebrón JA, Busico MP, Lanucara P, Spigler R (2005) Domain decomposition solution of elliptic boundary-value problems. SIAM J Sci Comput 27(2):440–457 zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Acebrón JA, Busico MP, Lanucara P, Spigler R (2005) Probabilistically induced domain decomposition methods for elliptic boundary-value problems. J Comput Phys 210(2):421–438 zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Acebrón JA, Spigler R (2005) Fast simulations of stochastic differential systems. J Comput Phys 208:106–115 zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Childress S (1981) Mechanics of swimming and flying, cambridge studies in mathematical biology, 2. Cambridge University Press, Cambridge Google Scholar
  5. 5.
    Fagg G, Bukovsky A, Dongarra J (2001) Harness and fault tolerant MPI. Parallel Comput 27:1479–1495 zbMATHCrossRefGoogle Scholar
  6. 6.
    Farhat C, Chandesris M (2003) Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications. Int J Numer Meth Eng 58:1397–1434 zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Graham SL, Snir M, Patterson CA (eds) (2004) Getting up to speed. The future of supercomputing. Report of National Research Council of the National Academies Sciences, The National Academies Press, Washington, DC, 2004. http://www.nap.edu
  8. 8.
    Geist A, Engelmann C (2005) Super-scalable algorithms for computing on 100,000 processors. In: Lecture Notes in Computer Science, Springer, vol 3514, April 2005, pp 313–321 Google Scholar
  9. 9.
  10. 10.
    Keyes DE (1998) How scalable is domain decomposition in practice? In: 11th Int conf on domain decomposition methods, London 1998. http://www.ddm.org
  11. 11.
    Keyes DE (2002) Domain decomposition in the mainstream of computational science. In: 14th Int conf on domain decomposition methods, Morelos, México, 2002. http://www.ddm.org
  12. 12.
    Lions JL, Maday Y, Turinici G (2001) A parareal in time discretization of PDE’s. C.R. Acad Sci Paris 332:661–668 zbMATHMathSciNetGoogle Scholar
  13. 13.
    Nielsen MA, Chuang IL (2000) Quantum computation and information. Cambridge University Press, Cambridge zbMATHGoogle Scholar
  14. 14.
    Nielsen MA, Dowling MR, Gu M, Doherty AC (2006) Quantum computation as geometry, Sci 311(24 February):1133–1135 Google Scholar
  15. 15.
    Parolini N, Quarteroni A (2005) Mathematical models and numerical simulations for the America’s Cup. Comput Methods Appl Mech Eng 194 (9–11):1001–1026 zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Shor PW (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J Comput 26:1484–1509 zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Shimasaki M, Zima HP (2004) The earth simulator, guest editorial, Parallel Comput 30(12):1277–1278 Google Scholar
  18. 18.
    Special issue on Distributed Computing (2005) Sci 308(6 May) Google Scholar
  19. 19.
    Vidal G (2003) Efficient classical simulation of slightly entangled quantum computations. Phys Rev Lett 91:147902 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Departament d’Enginyeria Informàtica i MatemàtiquesUniversitat Rovira i VirgiliTarragonaSpain
  2. 2.Dipartimento di MatematicaUniversità “Roma Tre”RomeItaly

Personalised recommendations