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Book Description

The aim of this book is to give a broad overview of the TLM (Transmission Line Matrix) method, which is one of the "time-domain numerical methods". These methods are reputed for their significant reliance on computer resources. However, they have the advantage of being highly general.

The TLM method has acquired a reputation for being a powerful and effective tool by numerous teams and still benefits today from significant theoretical developments. In particular, in recent years, its ability to simulate various situations with excellent precision, including complex materials, has been demonstrated.

Application examples are included in the last two chapters of the book, enabling the reader to draw conclusions regarding the performance of the implemented techniques and, at the same time, to validate them.

Contents

1. Basis of the TLM Method: the 2D TLM Method.

2. 3D Nodes.

3. Introduction of Discrete Elements and Thin Wires in the TLM Method.

4. The TLM Method in Matrix Form and the Z Transform.

Appendix A. Development of Maxwell's Equations using the Z Transform with a Variable Mesh.

Appendix B. Treatment of Plasma using the Z Transform for the TLM Method.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Introduction
  5. Chapter 1: Basis of the TLM Method: the 2D TLM Method
    1. 1.1. Historical introduction
    2. 1.2. 2D simulation
    3. 1.3. The TLM process
  6. Chapter 2: 3D Nodes
    1. 2.1. Historical development
    2. 2.2. The generalized condensed node [TRE 95b]
    3. 2.3. Time step
    4. 2.4. Dispersion of 3D nodes
    5. 2.5. Absorbing walls
    6. 2.6. Orthogonal curvilinear mesh [YOU 08]
    7. 2.7. Non-Cartesian nodes
  7. Chapter 3: Introduction of Discrete Elements and Thin Wires in the TLM Method
    1. 3.1. Introduction of discrete elements [BIS 99]
    2. 3.2. Introduction of thin wires [LAR 06]
  8. Chapter 4: The TLM Method in Matrix Form and the Z Transform
    1. 4.1. Introduction
    2. 4.2. Matrix form of Maxwell’s equations
    3. 4.3. Cubic mesh normalized Maxwell’s equations
    4. 4.4. The propagation process
    5. 4.5. Wave-matter interaction
    6. 4.6. The normalized parallelepipedic mesh Maxwell’s equations [LOU 04]
    7. 4.7. Application example: plasma modeling [MOU 06]
    8. 4.8. Conclusion
  9. APPENDICES
    1. Appendix A. Development of Maxwell’s Equations using the Z Transform with a Variable Mesh
    2. Appendix B. Treatment of Plasma using the Z Transform for the TLM Method
  10. Bibliography
  11. Index
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