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

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 botto...

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Bibliographic Details
Published in:Applied mathematics and computation 2002-08, Vol.130 (2), p.311-316
Main Authors: Katti, C.P., Srivastava, D.K., Sivaloganathan, S.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Finite difference
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Hypercube
Mathematical analysis
Mathematics
Navier–Stokes equation
Numerical analysis
Numerical analysis. Scientific computation
Parallel algorithm
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Physics
Sciences and techniques of general use
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(01)00098-4