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.

This book presents the topic in electromagnetics known as Transmission-Line Modeling or Matrix method-TLM. While it is written for engineering students at graduate and advanced undergraduate levels, it is also highly suitable for specialists in computational electromagnetics working in industry, who wish to become familiar with the topic. The main method of implementation of TLM is via the time-domain differential equations, however, this can also be via the frequency-domain differential equations. The emphasis in this book is on the time-domain TLM. Physical concepts are emphasized here before embarking onto mathematical development in order to provide simple, straightforward suggestions for the development of models that can then be readily programmed for further computations. Sections with strong mathematical flavors have been included where there are clear methodological advantages forming the basis for developing practical modeling tools. The book can be read at different depths depending on the background of the reader, and can be consulted as and when the need arises.

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 Compu

Written by renowned researcher Christos Christopoulos, this book covers a broad area of electromagnetics, including microwaves, antennas, radar cross-section, electromagnetic compatibility, and electromagnetic heating. In addition, you will find a clear explanation of modeling principles from lumped components through one-, two, and three-dimensional complex systems.

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® 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.