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Bi-CGSTAB for collocation equations on distributed memory parallel architectures

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • E. N. Mathioudakis

    (Technical University of Crete, Applied Mathematics and Computers Laboratory, Department of Sciences)

  • E. P. Papadopoulou

    (Technical University of Crete, Applied Mathematics and Computers Laboratory, Department of Sciences)

  • Y. G. Saridakis

    (Technical University of Crete, Applied Mathematics and Computers Laboratory, Department of Sciences)

Abstract

Summary In this paper, which extends and concludes our work in [3, 4], we deal with the problem of efficiently organizing the computation involved in the bi-conjugate gradient stabilized [5] iterative solution of large linear systems, in order to compute on a distributed memory parallel computer. These linear systems are associated with the discreti zation of elliptic boundary value problems using a collocation finite element method based on Hermite bi-cubic elements. The organization of the computation involved follows the methodology used in [3,4]. That is, having the collocation matrix in its normal 2-cyclic or red-black form for increased scalability, we map the computation involved on an appropriate virtual architecture which, in the sequel, is optimally repartitioned and mapped on to a fixed size architecture. The whole process leads to the development of an efficient and well-structured parallel algorithm. For demonstration purposes the algorithm was realized on a distributed memory Parsytee Cognitive computer CC-2.

Suggested Citation

  • E. N. Mathioudakis & E. P. Papadopoulou & Y. G. Saridakis, 2003. "Bi-CGSTAB for collocation equations on distributed memory parallel architectures," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 957-966, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_87
    DOI: 10.1007/978-88-470-2089-4_87
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