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

摘要

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.