Highly efficient parallel algorithm for finite difference solution to Navier-Stokes equation on a hypercube. (Q1855744)

It has been shown in [Nucl. Sci. Eng. 93, 6799 (1986)] that the finite difference discretization of Navier-Stokes equation leads to the solution of \(N\times N\) 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 \textit{J. Kowalik} [High Speed Computation, Springer (1984; Zbl 0577.68004)] is developed which decomposes the above matrix system into smaller quasi-tridiagonal \((p+1)\times (p+1)\) subsystem, which is then solved in Phase II using an odd-even reduction method.