A Parallel Non-square Tiled Algorithm for Solving a Kind of BVP for Second-Order ODEs

  • Przemysław Stpiczyński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6067)

Abstract

The aim of this paper is to show that a kind of boundary value problem for second-order ordinary differential equations which reduces to the problem of solving tridiagonal system of linear equations with almost Toeplitz structure can be efficiently solved on modern multicore architectures using a parallel tiled algorithm based on the divide and conquer approach for solving linear recurrence systems with constant coefficients and novel data formats for dense matrices.

Keywords

BVP for ODEs parallel non-square tiled algorithm multicore novel data formats for dense matrices 

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References

  1. 1.
    Buttari, A., Langou, J., Kurzak, J., Dongarra, J.: A class of parallel tiled linear algebra algorithms for multicore architectures. Parallel Computing 35, 38–53 (2009)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Chandra, R., Dagum, L., Kohr, D., Maydan, D., McDonald, J., Menon, R.: Parallel Programming in OpenMP. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  3. 3.
    Gustavson, F.G.: New generalized data structures for matrices lead to a variety of high performance algorithms. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 418–436. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Scott, L.R., Clark, T., Bagheri, B.: Scientific Parallel Computing. Princeton University Press, Princeton (2005)MATHGoogle Scholar
  5. 5.
    Stpiczyński, P.: Solving linear recurrence systems using level 2 and 3 BLAS routines. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2004. LNCS, vol. 3019, pp. 1059–1066. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    Stpiczyński, P.: Solving a kind of boundary value problem for ODEs using novel data formats for dense matrices. In: Ganzha, M., Paprzycki, M., Pełech-Pilichowski, T. (eds.) Proceedings of the International Multiconference on Computer Science and Information Technology, vol. 3, pp. 293–296. IEEE Computer Society Press, Los Alamitos (2008)CrossRefGoogle Scholar
  7. 7.
    Stpiczyński, P., Paprzycki, M.: Fully vectorized solver for linear recurrence systems with constant coefficients. In: Proceedings of VECPAR 2000 - 4th International Meeting on Vector and Parallel Processing, Porto, pp. 541–551. Facultade de Engerharia do Universidade do Porto (June 2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Przemysław Stpiczyński
    • 1
  1. 1.Department of Computer ScienceMaria Curie–Skłodowska UniversityLublinPoland

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