Reduction of Interconnected One-Dimensional Blocks of Nodes: Algorithm and Applications

Abstract

This article presents algorithms for solving discretized equations, originating from finite-volume, finite-element, or similar methods, over domains displaying an interconnected network of one-dimensional blocks of nodes. The algorithm derives coefficients connecting the root nodes of the one-dimensional blocks directly, thus eliminating the need for simultaneous solution of the intermediate nodes. Successive applications of the algorithm can reduce a complicated network of one-dimensional blocks into a single loop amenable to direct solution by the efficient tri-diagonal or cyclic-tri-diagonal algorithms. The article also demonstrates the algorithm’s application to an unsteady heat conduction problem and cites several areas in which it may be employed advantageously.

Key Words:

• TDMA
• networks
• cyclic reductions
• linear equation solvers

Additional information

Notes on contributors

M.A. Serag-Eldin

Mohamed Avar Serag-Eldin obtained his B.Sc. (mech. power eng.) in 1970 and his M.Sc. (mech. eng.) in 1973, both from Cairo University, Egypt; and his Ph.D. from Imperial College, London University, in 1977. He is Professor of Thermo-fluids and Chair of the Mechanical Engineering Department, American University in Cairo, Egypt. His research interests are computational fluid dynamics.