Transmission Line Method (TLM) or Transmission Line Matrix method is an elegant technique used to solve lossless or lossy wave equations. Here I am gathering together resources on the topic since I have found it is not well studied in the US.

Books

Christopoulos, Christos. “The transmission-line modeling (TLM) method in electromagnetics.” Synthesis Lectures on Computational Electromagnetics 1.1 (2005): 1-132. ISBN: 1598290509

This book is focused on the point of view of electrical engineering.

De Cogan, Donard. Transmission line matrix (TLM) techniques for diffusion applications. Gordon and Breach Science Publishers, 1998. ISBN: 978-9056991296

De Cogan, Donard, William J. O’Connor, and Susan Pulko. Transmission line matrix (TLM) in computational mechanics. CRC Press, 2005. ISBN: 978-0415327176

This is the book I found easiest to read from a Mechanical Engineering perspective. The book starts by looking at the wave equation in 1D. It uses the ideas of boundary conditions to explain the scattering effect that occurs in TLM. It is an easy read for an engineer who has studied the wave equation before.

Papers

Webpages

http://dandadec.com/what-is-tlm/ – This page is Donard De Cogan’s page. Donard’s website has lots of information on TLM such as conferences and papers.