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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.
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