Transmission Line Matrix (TLM) is a numerical technique which is based upon establishing an analogue between a space and time dependent physical problem and an electrical network which includes transmission lines. By their very nature these enforce time discretization on the network which can then be solved explicitly in the time-domain.
Although it is best known in electromagnetic applications, TLM can also be used to model diffusion phenomena, and this book outlines the state of the art in this area.
The first part of the book deals with theory and techniques. The second part is devoted to the development of algorithms for specific applications. This is arranged as a historical sequence starting with heat-flow and matter diffusion. The remainder of the book outlines many of the ingenious exploitations of the unique properties of TLM, including topics such as the solution of convection, Poisson, Laplace, and time-dependent Schrodinger equations. Applications in the firing of ceramics, chromatography, image processing, and the solution of inverse thermal problems are also covered.

The finite element method reigns as the dominant technique for modeling mechanical systems. Originally developed to model electromagnetic systems, the Transmission Line Matrix (TLM) method proves to match, and in some cases exceed, the effectiveness of finite elements for modeling several types of physical systems. Transmission Line Matrix in Computational Mechanics provides a tutorial approach to applying TLM for modeling mechanical and other physical systems. Transmission Line Matrix in Computational Mechanics begins with the history of TLM, an introduction to the theory using mechanical engineering concepts, and the electromagnetic basics of TLM. The authors then demonstrate the theory for use in acoustic propagation, along with examples of MATLAB(R) code. The remainder of the book explores the application of TLM to problems in mechanics, specifically heat and mass transfer, elastic solids, simple deformation models, hydraulic systems, and computational fluid dynamics. A discussion of state-of-the-art techniques concludes the book, offering a look at the current research undertaken by the authors and other leading experts to overcome the limitations of TLM in applying the method to diverse types of systems. This valuable reference introduces students, engineers, and researchers to a powerful, accurate, and stable alternative to finite elements, providing case studies and examples to reinforce the concepts and illustrate the applications.

A good mathematical model of a physical situation leads to improved understanding. A good model must be robust (its underlying assumptions must not lead to inconsistent results) and it must be predictive anticipating results that can be verified by experiment. This book shows engineers how to construct or choose such models and how to solve them numerically. These are enormously important tasks in practical engineering.