Highly efficient parallel algorithm for finite difference solution to Navier--Stoke's equation on a hypercube

  • Authors:

  • C. P. Katti;D. K. Srivastava;S. Sivaloganathan

  • Affiliations:

  • School of Computer and System Sciences, Jawaharlal Nehru University, New Delhi, India;School of Computer and System Sciences, Jawaharlal Nehru University, New Delhi, India;Department of Applied Mathematics, University of Waterloo, Waterloo, Ont., Canada N2L 3G1

  • Venue:
  • Applied Mathematics and Computation
  • Year:
  • 2002

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Abstract

It has been shown in [Nuclear Science and Engineering 93 (1986) 6799] that the finite difference discretization of Navier-Stoke's equation leads to the solution of N × N system written in the matrix form as My = B, where M is a quasi-tridiagonal having non-zero elements at the top right and bottom left corners. We present an efficient parallel algorithm on a p-processor hypercube implemented in two phases. In phase I a generalization of an algorithm due to Kowalik [High Speed Computation, Springer, New York] is developed which decomposes the above matrix system into smaller quasi-tridiagonal (p + 1) × (p + 1) subsystem, which is then solved in Phase II using an odd-even reduction method.