Electromagnetic Simulation Using the FDTD Method with Python (eBook)

Jennifer E. Houle is the Vice President for Research at Moscow-Berlin Simulations. She also worked as a Senior Product Engineer at Micron Technology. She has a Masters degree in Electrical Engineering from the University of Idaho. Her work has been published in the International Journal of Magnetics and Electromagnetism and the Symposium on Nonlinear Optics and Sum Rules, and her research was presented at the 32nd Annual Meeting of the European Hyperthermic Oncology Society. Dennis M. Sullivan, PhD, is Professor of Electrical and Computer Engineering at the University of Idaho. His research interests are electromagnetic and quantum simulation, and include hyperthermia cancer therapy, nonlinear optical simulation, and quantum semiconductor simulation. In 2013 he was made a fellow of the Institute of Electrical and Electronic Engineers. He published the first edition of Electromagnetic Simulation Using the FDTD Method with Wiley in 2001 and the second edition in 2013.

About the Authors ix

Preface xi

Guide to the Book xiii

1 One-Dimensional Simulation with the FDTD Method 1

1.1 One-Dimensional Free-Space Simulation 1

1.2 Stability and the FDTD Method 5

1.3 The Absorbing Boundary Condition in One Dimension 6

1.4 Propagation in a Dielectric Medium 7

1.5 Simulating Different Sources 9

1.6 Determining Cell Size 10

1.7 Propagation in a Lossy Dielectric Medium 11

1.A Appendix 14

References 15

2 More on One-Dimensional Simulation 25

2.1 Reformulation Using the Flux Density 25

2.2 Calculating the Frequency Domain Output 28

2.3 Frequency-Dependent Media 31

2.3.1 Auxiliary Differential Equation Method 35

2.4 Formulation Using Z Transforms 37

2.4.1 Simulation of Unmagnetized Plasma 38

2.5 Formulating a Lorentz Medium 41

2.5.1 Simulation of Human Muscle Tissue 45

References 47

3 Two-Dimensional Simulation 59

3.1 FDTD in Two Dimensions 59

3.2 The Perfectly Matched Layer (PML) 62

3.3 Total/Scattered Field Formulation 72

3.3.1 A Plane Wave Impinging on a Dielectric Cylinder 74

3.3.2 Fourier Analysis 76

References 78

4 Three-Dimensional Simulation 99

4.1 Free-Space Simulation 99

4.2 The PML in Three Dimensions 103

4.3 Total/Scattered Field Formulation in Three Dimensions 105

4.3.1 A Plane Wave Impinging on a Dielectric Sphere 107

References 111

5 Advanced Python Features 129

5.1 Classes 129

5.1.1 Named Tuples 131

5.2 Program Structure 133

5.2.1 Code Repetition 133

5.2.2 Overall Structure 135

5.3 Interactive Widgets 136

6 Deep Regional Hyperthermia Treatment Planning 159

6.1 Introduction 160

6.2 FDTD Simulation of the Sigma 60 161

6.2.1 Simulation of the Applicator 161

6.2.2 Simulation of the Patient Model 163

6.3 Simulation Procedure 165

6.4 Discussion 168

References 170

Appendix A The Z Transform 171

Appendix B Analytic Solution to Calculating the Electric Field 183

Index 195