Parallel solution of closely coupled systems

An odd-even permutation and a nested dissection technique were used to circumvent the strong seriality of a system of closely coupled equations. The effect of transforming the n x n Hermitian definite positive matrix coefficient on the topology of Cholesky factors is discussed. A series of directed graphs is constructed in order to show the computational steps required for the odd-even permutation. Numerical expressions for the speed-up and efficiency of parallel N-processing techniques and sequential processing by a single computer are derived. Similar expressions are derived for the case of insufficient processing capacity. The application of the odd-even permutation to the ensemble class of computer architectures is demonstrated.